1. The document discusses electric fields, including field vectors, field strengths for point charges and uniform fields, and fields around various charge configurations.
2. It reviews gravitational fields and compares them to electric fields. Both fields are defined by the force per unit charge or mass exerted on a test particle.
3. Examples are given of calculating field strengths and drawing electric field lines for single and multiple point charges of the same and opposite signs.
1) The document reviews electric fields, including field vectors, field strengths for point charges and uniform fields, and work done by electric fields.
2) It compares electric fields to gravitational fields, noting that electric field lines emanate from positive charges and penetrate negative charges.
3) Examples are given of drawing the electric field for single and multiple point charges, as well as charges of different magnitudes and equal but opposite charges.
1. Michael Faraday developed the concept of an electric field as a property of space around a charged object that causes forces on other charged objects. The electric field at a point is defined as the force on a test charge divided by the test charge.
2. Electric field lines represent the direction of the electric field, with closer lines indicating a stronger field. The electric field due to multiple charges is the vector sum of the individual fields.
3. Electric potential difference (voltage) is defined as the change in electric potential energy of a charge divided by the charge, and represents the work required to move a charge between two points against the electric field.
The document discusses electric potential and potential energy. Some key points:
1) Electric potential (V) at a point is the work required to move a small positive test charge to that point from infinity without any net external force.
2) Lines of equipotential connect all points of equal electric potential. Charged particles placed at these points will not experience a force or change in potential energy.
3) The electric potential due to a point charge can be calculated using the work done to move a test charge from infinity to that point. Potential increases as distance from the charge decreases.
4) At locations of zero potential, like point P in one example, a field can still exist. A
Electric fields arise from charged objects and can exert forces on other charged objects. There are two types of electric charge: positive and negative. Electric field lines show the direction that a positive test charge would move due to the electric field. Electric fields are generated by both positive and negative charges, and the strength of the electric field depends on the magnitude of the charges and the distance between them, as described by Coulomb's law. The electric field strength is defined as the force per unit charge exerted by the field on a small test charge placed within it.
The document discusses electric fields and electrostatics. It explains that when objects are rubbed together, electrons are transferred causing objects to become charged. It then discusses Coulomb's law which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It provides equations for calculating electric field strength, potential, and force experienced by charges in fields.
Okay, let's break this down step-by-step:
1) The electric field E is uniform, so E has a constant magnitude and direction.
2) The path icf consists of two segments: ic and cf.
3) For ic, the displacement is at a 90° angle to E so no work is done along that segment.
4) For cf, the displacement forms a 45° angle with E.
So the key is to integrate E×ds along just the cf segment.
The document defines key concepts relating to electric fields and potential. It defines an electric field as the space around a charge where another charge feels a force, and represents electric fields using field lines showing direction and strength. Electric field strength is defined as the force felt by 1 coulomb of charge, and can be calculated as force over charge. A charge placed in a uniform electric field will experience a force in the direction or opposite the field depending on its sign. The strength of a uniform electric field is calculated as the potential difference across plates over their separation. The radial electric field of a point charge is defined, and its strength calculated using Coulomb's law as force over test charge. Electric potential is defined as the electric potential energy of
The document summarizes key concepts about electric potential and electric potential energy. It defines electric potential as the work required per unit charge to move a charge from a reference point to its current position in an electric field. Electric potential energy is defined as stored energy in a charge-field system due to the charges' positions. The document outlines how electric potential and potential energy relate to work, electric fields, and voltage. It also discusses applications of these concepts, including conductors, equipotential surfaces, and the Bohr model of the hydrogen atom.
1) The document reviews electric fields, including field vectors, field strengths for point charges and uniform fields, and work done by electric fields.
2) It compares electric fields to gravitational fields, noting that electric field lines emanate from positive charges and penetrate negative charges.
3) Examples are given of drawing the electric field for single and multiple point charges, as well as charges of different magnitudes and equal but opposite charges.
1. Michael Faraday developed the concept of an electric field as a property of space around a charged object that causes forces on other charged objects. The electric field at a point is defined as the force on a test charge divided by the test charge.
2. Electric field lines represent the direction of the electric field, with closer lines indicating a stronger field. The electric field due to multiple charges is the vector sum of the individual fields.
3. Electric potential difference (voltage) is defined as the change in electric potential energy of a charge divided by the charge, and represents the work required to move a charge between two points against the electric field.
The document discusses electric potential and potential energy. Some key points:
1) Electric potential (V) at a point is the work required to move a small positive test charge to that point from infinity without any net external force.
2) Lines of equipotential connect all points of equal electric potential. Charged particles placed at these points will not experience a force or change in potential energy.
3) The electric potential due to a point charge can be calculated using the work done to move a test charge from infinity to that point. Potential increases as distance from the charge decreases.
4) At locations of zero potential, like point P in one example, a field can still exist. A
Electric fields arise from charged objects and can exert forces on other charged objects. There are two types of electric charge: positive and negative. Electric field lines show the direction that a positive test charge would move due to the electric field. Electric fields are generated by both positive and negative charges, and the strength of the electric field depends on the magnitude of the charges and the distance between them, as described by Coulomb's law. The electric field strength is defined as the force per unit charge exerted by the field on a small test charge placed within it.
The document discusses electric fields and electrostatics. It explains that when objects are rubbed together, electrons are transferred causing objects to become charged. It then discusses Coulomb's law which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It provides equations for calculating electric field strength, potential, and force experienced by charges in fields.
Okay, let's break this down step-by-step:
1) The electric field E is uniform, so E has a constant magnitude and direction.
2) The path icf consists of two segments: ic and cf.
3) For ic, the displacement is at a 90° angle to E so no work is done along that segment.
4) For cf, the displacement forms a 45° angle with E.
So the key is to integrate E×ds along just the cf segment.
The document defines key concepts relating to electric fields and potential. It defines an electric field as the space around a charge where another charge feels a force, and represents electric fields using field lines showing direction and strength. Electric field strength is defined as the force felt by 1 coulomb of charge, and can be calculated as force over charge. A charge placed in a uniform electric field will experience a force in the direction or opposite the field depending on its sign. The strength of a uniform electric field is calculated as the potential difference across plates over their separation. The radial electric field of a point charge is defined, and its strength calculated using Coulomb's law as force over test charge. Electric potential is defined as the electric potential energy of
The document summarizes key concepts about electric potential and electric potential energy. It defines electric potential as the work required per unit charge to move a charge from a reference point to its current position in an electric field. Electric potential energy is defined as stored energy in a charge-field system due to the charges' positions. The document outlines how electric potential and potential energy relate to work, electric fields, and voltage. It also discusses applications of these concepts, including conductors, equipotential surfaces, and the Bohr model of the hydrogen atom.
This document provides an overview of electrostatics and electric fields. It discusses frictional electricity, properties of electric charges, Coulomb's law, units of charge, and continuous charge distributions. It also covers electric fields, electric field intensity due to point charges, the superposition principle, electric field lines, electric dipoles, and properties of electric field lines. The key topics covered in 3 sentences or less are: Electrostatic forces arise from the transfer of electrons when two materials are rubbed together. Coulomb's law describes the electrostatic force between point charges, which depends on the product of the charges and inversely on the square of the distance between them. Electric field lines represent the direction and strength of the electric field and eman
1) Point charges placed in space create electric fields that exert forces on other charges, either attracting or repelling them.
2) The electric field concept can explain how charges interact at a distance.
3) Coulomb's law describes the electrostatic force between two point charges quantitatively in terms of the charges and their distance.
1. A field is defined as a property of space in which a material object experiences a force. For example, above the earth there is a gravitational field where a mass experiences a downward force.
2. The electric field is a vector field that exists around an electric charge even when no other charges are present. The direction of the electric field points away from a positive charge and towards a negative charge.
3. The electric field strength is defined as the force experienced by a hypothetical positive test charge per unit of charge, located at that point in space.
Electric potential is defined as the electric potential energy per unit charge. It is measured in volts and represents the work required to move a charge between two points. The electric potential difference between two points is equal to the work needed to move a positive test charge between those points. Equipotential surfaces represent points in space where the electric potential is the same. Electric field lines are always perpendicular to equipotential surfaces.
- Electric charge is quantized and can only exist in integer multiples of the elementary charge of electrons and protons. Charge is conserved in nuclear decay processes.
- Coulomb's law describes the electric force between two point charges. The electric field is defined as the force per unit charge exerted on a test charge. Gauss's law relates the net electric flux through a closed surface to the enclosed charge.
- The electric field due to symmetric charge distributions like point charges, spherical charge distributions, and charged plates can be calculated using Gauss's law. This allows determining electric fields without calculating the contributions of individual charges.
This document provides an overview of electrostatics and related concepts in physics. It defines electrostatics as dealing with charges at rest and their properties. Key topics covered include the historical discovery of static electricity, the conservation and quantization of electric charge, electric fields and lines of force, electric dipoles, capacitance, and devices like the Van de Graff generator. Concepts are explained through definitions, diagrams, and mathematical equations.
The document discusses electric field, potential, and energy. It defines electric potential as the work done to move a unit positive charge from infinity to a point in an electric field. Electric potential is a scalar quantity measured in volts. Equipotentials are regions in space where the electric potential has a constant value, forming equipotential surfaces or lines. Analogies are drawn between electric and gravitational fields, such as both following inverse square laws and having field lines and equipotentials.
- An equipotential surface is a surface where all points have the same electric potential. For a point charge, equipotential surfaces are concentric spherical surfaces. For a uniform electric field, equipotential surfaces form planes perpendicular to the field.
- The electric field is always perpendicular to equipotential surfaces. If it is not, work would be required to move a charge along the surface, contradicting the definition.
- Electrostatic potential energy of a system of point charges depends only on the distances between charges. It is equal to the work required to assemble the charges from infinity.
1) The document discusses electric force and field, explaining that an electric field exists in the space surrounding charged objects and is a property of those charged sources.
2) It provides examples of the magnitude of electric fields in different situations, from household circuits to inside atoms.
3) The electric field due to a point charge is illustrated as radiating uniformly outward or inward from the charge, depending on its sign.
Ppt djy 2011 topic 5.1 electric potential difference slDavid Young
The document discusses electric potential difference and electric potential energy. It defines electric potential difference as the work done per unit charge when moving a charge between two points in an electric field. This can also be thought of as the change in electric potential energy per unit charge. Electric potential difference is measured in volts, where 1 volt is equal to 1 joule per coulomb. Examples and practice problems are provided to illustrate these concepts and how to calculate electric potential difference, electric field strength, and changes in electric potential energy.
Gauss's law relates the electric flux through a closed surface to the electric charge enclosed by the surface. It can be used to calculate the electric field due to various charge distributions like:
- A point charge, where the electric field is spherically symmetric and directed radially outward.
- An infinite line charge, where the electric field is directed radially outward and its magnitude depends only on the distance from the wire.
- An infinite plane sheet, where the electric field is uniform and perpendicular to the sheet.
- Two parallel charged sheets, where the electric field is zero outside and uniform inside, directed from the positive to negative sheet.
- A charged spherical shell, where the electric field
1. The document discusses electric fields created by point charges and electric dipoles. It defines electric field strength and describes how electric field strength is calculated for point charges and dipoles.
2. Key properties of electric field lines are outlined, including that they emanate from positive charges and terminate at negative charges.
3. Formulas are given for calculating the torque and work done on an electric dipole placed in a uniform electric field. The dipole will experience a torque causing it to rotate into alignment with the field.
Electrostatic potential and capacitanceEdigniteNGO
Hello everyone, we are from Edignite NGO and we have come up with chapters of class 11 and 12 (CBSE).
For any queries, please contact
Lekha Periwal : +916290889619
Heer Mehta : +917984844099
- Early experiments in magnetism date back to ancient Greeks and Chinese who observed magnetic properties.
- In the 13th century, Pierre de Maricourt discovered magnetic field lines and the existence of magnetic poles.
- In the 1820s, experiments by Faraday, Henry and others established the connection between electricity and magnetism.
- A magnetic field is generated by moving electric charges or magnetic materials. It exerts a force on moving charges perpendicular to both the field and velocity vectors.
- The motion of a charged particle in a magnetic field follows a circular or helical path depending on its orientation to the field.
George Cross Electromagnetism Electric Field Lecture27 (2)George Cross
Electric field, field of multiple charges, field of continuous charge, parallel plate capacitor, motion of charge in electric field, motion of dipole in field
*Animated PPT FOR SCHOOL/ Coachings *
Physics , Chemistry , maths , biology
(Improve your teaching style )
*CONTENT*:-
1. ANIMATED THEORY
(COMES ON PRESS KEY ONE BY ONE )
2.MCQ
3. LIVE EXAMPLE
4. ANIMATED IMAGES LIKE
SPRING , CAR ETC
5. ANIMATED
6. CHAPTER WISE QUESTIONS AND SOLUTION WITH ANIMATED IMAGES
7. SEPARATE TOPIC SEPARATE FILES
Live example watch this video
https://youtu.be/PG4LTFUKi1A
https://drive.google.com/folderview?id=1KsUPQfeqPQXQ6y6MzoMl07C89yRYhnQt
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1. The document discusses various topics in electrostatics including line integrals of electric fields, electric potential and potential differences, Gauss's theorem, and applications of Gauss's theorem.
2. Key concepts covered are the definitions of electric potential and potential difference, the relationship between electric field and potential via line integrals, and Gauss's theorem that the electric flux through any closed surface is equal to the enclosed charge divided by the permittivity of free space.
3. Examples are given of using Gauss's theorem to calculate electric fields, such as for an infinite line charge, planar sheet of charge, and spherical shell of charge.
Class 12th Physics Electrostatics part 2Arpit Meena
This document discusses the concepts of electrostatics including electric field, electric field intensity, and electric field lines. It defines electric field as a region around charged particles where other charges will experience a force. Electric field intensity is the force per unit charge on a small test charge. The electric field due to a point charge is defined by the equation E=kq/r^2 and has spherical symmetry. The superposition principle states that the total electric field is the vector sum of the fields due to individual charges. Electric field lines are imaginary lines showing the direction of the electric field. Key properties of electric field lines are also discussed. The document further explains the electric field due to an electric dipole, and the torque and work
1. Electrostatic potential is defined as the work done per unit charge to bring a test charge from infinity to a point in an electric field.
2. The electric potential at a point due to a single point charge is directly proportional to the charge and inversely proportional to the distance from the charge.
3. The electric potential at a point due to multiple charges is equal to the sum of the potentials due to each individual charge.
Electric fields are regions where charged particles experience forces. The strength of an electric field is defined by the force it exerts on a test charge placed within the field and can be calculated using the formula E=F/q, where E is electric field strength, F is the force on the test charge, and q is the charge of the test charge. The direction of the electric field is defined as the direction in which a positive test charge would experience force.
The document discusses electric field lines and their properties. It provides examples of electric field line patterns for single and multiple point charges. Key points covered include:
- Electric field lines extend radially outward from a positive point charge and inward toward a negative point charge.
- For two charges of the same sign, field lines point from one charge to the other with no lines between. For opposite charges, field lines begin on the positive and end on the negative charge.
- The number of field lines is proportional to charge magnitude. Stronger fields have more closely spaced lines.
- Field lines always meet conductors perpendicularly and the field is zero inside a charged conductor.
This document provides an overview of electrostatics and electric fields. It discusses frictional electricity, properties of electric charges, Coulomb's law, units of charge, and continuous charge distributions. It also covers electric fields, electric field intensity due to point charges, the superposition principle, electric field lines, electric dipoles, and properties of electric field lines. The key topics covered in 3 sentences or less are: Electrostatic forces arise from the transfer of electrons when two materials are rubbed together. Coulomb's law describes the electrostatic force between point charges, which depends on the product of the charges and inversely on the square of the distance between them. Electric field lines represent the direction and strength of the electric field and eman
1) Point charges placed in space create electric fields that exert forces on other charges, either attracting or repelling them.
2) The electric field concept can explain how charges interact at a distance.
3) Coulomb's law describes the electrostatic force between two point charges quantitatively in terms of the charges and their distance.
1. A field is defined as a property of space in which a material object experiences a force. For example, above the earth there is a gravitational field where a mass experiences a downward force.
2. The electric field is a vector field that exists around an electric charge even when no other charges are present. The direction of the electric field points away from a positive charge and towards a negative charge.
3. The electric field strength is defined as the force experienced by a hypothetical positive test charge per unit of charge, located at that point in space.
Electric potential is defined as the electric potential energy per unit charge. It is measured in volts and represents the work required to move a charge between two points. The electric potential difference between two points is equal to the work needed to move a positive test charge between those points. Equipotential surfaces represent points in space where the electric potential is the same. Electric field lines are always perpendicular to equipotential surfaces.
- Electric charge is quantized and can only exist in integer multiples of the elementary charge of electrons and protons. Charge is conserved in nuclear decay processes.
- Coulomb's law describes the electric force between two point charges. The electric field is defined as the force per unit charge exerted on a test charge. Gauss's law relates the net electric flux through a closed surface to the enclosed charge.
- The electric field due to symmetric charge distributions like point charges, spherical charge distributions, and charged plates can be calculated using Gauss's law. This allows determining electric fields without calculating the contributions of individual charges.
This document provides an overview of electrostatics and related concepts in physics. It defines electrostatics as dealing with charges at rest and their properties. Key topics covered include the historical discovery of static electricity, the conservation and quantization of electric charge, electric fields and lines of force, electric dipoles, capacitance, and devices like the Van de Graff generator. Concepts are explained through definitions, diagrams, and mathematical equations.
The document discusses electric field, potential, and energy. It defines electric potential as the work done to move a unit positive charge from infinity to a point in an electric field. Electric potential is a scalar quantity measured in volts. Equipotentials are regions in space where the electric potential has a constant value, forming equipotential surfaces or lines. Analogies are drawn between electric and gravitational fields, such as both following inverse square laws and having field lines and equipotentials.
- An equipotential surface is a surface where all points have the same electric potential. For a point charge, equipotential surfaces are concentric spherical surfaces. For a uniform electric field, equipotential surfaces form planes perpendicular to the field.
- The electric field is always perpendicular to equipotential surfaces. If it is not, work would be required to move a charge along the surface, contradicting the definition.
- Electrostatic potential energy of a system of point charges depends only on the distances between charges. It is equal to the work required to assemble the charges from infinity.
1) The document discusses electric force and field, explaining that an electric field exists in the space surrounding charged objects and is a property of those charged sources.
2) It provides examples of the magnitude of electric fields in different situations, from household circuits to inside atoms.
3) The electric field due to a point charge is illustrated as radiating uniformly outward or inward from the charge, depending on its sign.
Ppt djy 2011 topic 5.1 electric potential difference slDavid Young
The document discusses electric potential difference and electric potential energy. It defines electric potential difference as the work done per unit charge when moving a charge between two points in an electric field. This can also be thought of as the change in electric potential energy per unit charge. Electric potential difference is measured in volts, where 1 volt is equal to 1 joule per coulomb. Examples and practice problems are provided to illustrate these concepts and how to calculate electric potential difference, electric field strength, and changes in electric potential energy.
Gauss's law relates the electric flux through a closed surface to the electric charge enclosed by the surface. It can be used to calculate the electric field due to various charge distributions like:
- A point charge, where the electric field is spherically symmetric and directed radially outward.
- An infinite line charge, where the electric field is directed radially outward and its magnitude depends only on the distance from the wire.
- An infinite plane sheet, where the electric field is uniform and perpendicular to the sheet.
- Two parallel charged sheets, where the electric field is zero outside and uniform inside, directed from the positive to negative sheet.
- A charged spherical shell, where the electric field
1. The document discusses electric fields created by point charges and electric dipoles. It defines electric field strength and describes how electric field strength is calculated for point charges and dipoles.
2. Key properties of electric field lines are outlined, including that they emanate from positive charges and terminate at negative charges.
3. Formulas are given for calculating the torque and work done on an electric dipole placed in a uniform electric field. The dipole will experience a torque causing it to rotate into alignment with the field.
Electrostatic potential and capacitanceEdigniteNGO
Hello everyone, we are from Edignite NGO and we have come up with chapters of class 11 and 12 (CBSE).
For any queries, please contact
Lekha Periwal : +916290889619
Heer Mehta : +917984844099
- Early experiments in magnetism date back to ancient Greeks and Chinese who observed magnetic properties.
- In the 13th century, Pierre de Maricourt discovered magnetic field lines and the existence of magnetic poles.
- In the 1820s, experiments by Faraday, Henry and others established the connection between electricity and magnetism.
- A magnetic field is generated by moving electric charges or magnetic materials. It exerts a force on moving charges perpendicular to both the field and velocity vectors.
- The motion of a charged particle in a magnetic field follows a circular or helical path depending on its orientation to the field.
George Cross Electromagnetism Electric Field Lecture27 (2)George Cross
Electric field, field of multiple charges, field of continuous charge, parallel plate capacitor, motion of charge in electric field, motion of dipole in field
*Animated PPT FOR SCHOOL/ Coachings *
Physics , Chemistry , maths , biology
(Improve your teaching style )
*CONTENT*:-
1. ANIMATED THEORY
(COMES ON PRESS KEY ONE BY ONE )
2.MCQ
3. LIVE EXAMPLE
4. ANIMATED IMAGES LIKE
SPRING , CAR ETC
5. ANIMATED
6. CHAPTER WISE QUESTIONS AND SOLUTION WITH ANIMATED IMAGES
7. SEPARATE TOPIC SEPARATE FILES
Live example watch this video
https://youtu.be/PG4LTFUKi1A
https://drive.google.com/folderview?id=1KsUPQfeqPQXQ6y6MzoMl07C89yRYhnQt
*Delivery in 1 min in Google drive*
No any file miss .
* Work with in zoom ,Google neet , *
contact/whatsapp:- 9753223223
1. The document discusses various topics in electrostatics including line integrals of electric fields, electric potential and potential differences, Gauss's theorem, and applications of Gauss's theorem.
2. Key concepts covered are the definitions of electric potential and potential difference, the relationship between electric field and potential via line integrals, and Gauss's theorem that the electric flux through any closed surface is equal to the enclosed charge divided by the permittivity of free space.
3. Examples are given of using Gauss's theorem to calculate electric fields, such as for an infinite line charge, planar sheet of charge, and spherical shell of charge.
Class 12th Physics Electrostatics part 2Arpit Meena
This document discusses the concepts of electrostatics including electric field, electric field intensity, and electric field lines. It defines electric field as a region around charged particles where other charges will experience a force. Electric field intensity is the force per unit charge on a small test charge. The electric field due to a point charge is defined by the equation E=kq/r^2 and has spherical symmetry. The superposition principle states that the total electric field is the vector sum of the fields due to individual charges. Electric field lines are imaginary lines showing the direction of the electric field. Key properties of electric field lines are also discussed. The document further explains the electric field due to an electric dipole, and the torque and work
1. Electrostatic potential is defined as the work done per unit charge to bring a test charge from infinity to a point in an electric field.
2. The electric potential at a point due to a single point charge is directly proportional to the charge and inversely proportional to the distance from the charge.
3. The electric potential at a point due to multiple charges is equal to the sum of the potentials due to each individual charge.
Electric fields are regions where charged particles experience forces. The strength of an electric field is defined by the force it exerts on a test charge placed within the field and can be calculated using the formula E=F/q, where E is electric field strength, F is the force on the test charge, and q is the charge of the test charge. The direction of the electric field is defined as the direction in which a positive test charge would experience force.
The document discusses electric field lines and their properties. It provides examples of electric field line patterns for single and multiple point charges. Key points covered include:
- Electric field lines extend radially outward from a positive point charge and inward toward a negative point charge.
- For two charges of the same sign, field lines point from one charge to the other with no lines between. For opposite charges, field lines begin on the positive and end on the negative charge.
- The number of field lines is proportional to charge magnitude. Stronger fields have more closely spaced lines.
- Field lines always meet conductors perpendicularly and the field is zero inside a charged conductor.
This document discusses electric fields, including Coulomb's law, electric field lines, and the motion of charged particles in electric fields. Some key points include:
- Coulomb's law describes the electrostatic force between two point charges and is analogous to Newton's law of universal gravitation.
- Electric field lines represent the strength and direction of an electric field graphically. They originate on positive charges and terminate on negative charges.
- Charged particles experience a force when moving through an electric field, causing them to accelerate. Their motion can be analyzed using concepts from kinematics.
The document discusses electric field lines and their properties. It provides examples of electric field line patterns for single and multiple point charges of both positive and negative polarity. Key points made include:
- Electric field lines extend radially outward from positive point charges and radially inward towards negative point charges.
- Between two same polarity charges, field lines point from one charge to the other with an absence of lines between. Between opposite charges, lines begin on one and end on the other.
- The number of field lines is proportional to charge magnitude. Higher line density means stronger field. Field direction is tangent to lines.
1) Gravitational and electric fields can be described by their field strength, which is defined as the force exerted per unit mass or charge.
2) Coulomb's law and Newton's law of gravitation describe the relationship between field strength and distance from the source of the field. Field strength decreases with the inverse square of the distance.
3) Electric and gravitational potential are scalar quantities that represent the potential energy per unit mass or charge. Potential increases as distance from the source decreases. Equipotential lines represent regions of constant potential.
1) Gravitational and electric fields can be described by their field strength, which is defined as the force exerted per unit mass or charge.
2) Gravitational field strength is calculated using Newton's law of universal gravitation, while electric field strength uses Coulomb's law.
3) The electric potential at a point is defined as the work required to move a unit charge from infinity to that point, and equipotentials are surfaces or lines of constant potential.
The document discusses electrostatics and provides information about an introductory physics course. It defines key concepts like Coulomb's law, electric fields, electric flux, and more. It gives examples and problems to illustrate these concepts. The instructor is Dr. Sabar Hutagalung and the main textbook is Physics for Scientists and Engineers by Serway and Jewett. The document outlines topics to be covered including charge, Coulomb's law, electric fields, Gauss's law, electric potential, and capacitors.
Electric charge is a fundamental property of matter that exists in two forms: positive or negative. Like charges repel and unlike charges attract. Charge is quantized and conserved within isolated systems. Conductors readily transmit charges through loosely bound outer electrons, while insulators do not transmit charges at all. Charged objects create electric fields that exert forces on other charges according to Coulomb's law. The electric field is defined as the force felt by a test charge placed at a given point. Field lines depict the direction and strength of the electric field. Within conductors, the electric field is zero and excess charge resides entirely on the surface. The field is strongest at sharp points on conductors.
The document describes concepts from a lecture on electric fields, including:
1. The electric field E at a point is defined as the electric force F on a test charge divided by the charge q. Field lines depict the direction and strength of the field.
2. The electric field due to a point charge is directed away from a positive charge and toward a negative charge.
3. The field of a dipole is non-uniform, exerting a torque and giving the dipole a potential energy depending on its orientation in the field.
4. Continuous charge distributions are treated by summing the contributions of small charge elements to the electric field.
The document describes concepts from a lecture on electric fields, including:
1. The electric field E at a point is defined as the electric force F on a test charge divided by the test charge q. Field lines depict the direction and strength of the electric field.
2. The electric field due to a point charge is directed away from a positive charge and toward a negative charge.
3. The field due to a dipole can be determined by treating it as two point charges. A dipole experiences a torque and potential energy in an external electric field based on its orientation.
chap ppt powerpoikslslakakkakakhwjwnt2.pptxmitakar7868
An equipotential surface is a surface where all points have the same electric potential. No work is required to move a charge between points on an equipotential surface since they are at the same potential. Equipotential surfaces corresponding to a field that uniformly increases in magnitude but remains constant in the z-direction will have decreasing separation between surfaces in the direction of increasing field, unlike the equidistant surfaces of a constant electric field.
The document discusses electrostatics and electric fields. It states that all charged objects have an electric field around them, which is a region where a test charge would experience a force. The electric field points in the direction that a positive test charge would move. The document then goes on to describe different patterns of electric fields, how field strength is calculated, and the elementary charge of an electron. It also discusses the principle of conservation of charge in closed systems.
An electron beam with a range of velocities enters a region with perpendicular electric and magnetic fields. Electrons with a specific velocity, v, will travel undeflected along the original path. Electrons with velocities slightly higher or lower than v will follow circular paths and be absorbed by the walls. This arrangement is called a velocity filter or selector, and selects a single velocity from the initial distribution. It works by balancing the electric and magnetic forces for electrons with velocity v, so they feel no net force. Slower and faster electrons respectively feel an unbalanced upward or downward force, causing deflection.
The document contains information about an upcoming mid-semester physics test, including the date, time, and location. It also provides checkpoint questions from previous lectures on topics like electric charge distribution and electric potential. Finally, it summarizes key concepts relating to electric potential, including definitions, calculations of potential for single and multiple point charges, and the relationship between potential and electric field.
The document contains information about an upcoming mid-semester physics test, including the date, time, and location. It also provides checkpoint questions from previous lectures on topics like electric charge distribution and electric potential. Finally, it summarizes key concepts relating to electric potential, including definitions, calculations of potential for single and multiple point charges, and the relationship between potential and electric field.
1. This document discusses electrostatic potential energy and electric potential. It defines electric potential energy as the minimum work needed to bring a charge to a point from infinity without acceleration in an electric field.
2. Electric potential (also called voltage) is defined as the work required to move a unit positive charge from a reference point to a specific point in an electric field. The electric potential at a point depends only on the position of that point and is independent of the path taken.
3. Equipotential surfaces are surfaces where the electric potential is constant at every point. Electric field lines are always perpendicular to equipotential surfaces.
This document provides an overview of electrostatics. It defines key concepts like electric field, electric flux density, Gauss's law, capacitance, and more. Applications of electrostatics include electric power transmission, X-ray machines, solid-state electronics, medical devices, industrial processes, and agriculture. Coulomb's law describes the electric force between point charges. Gauss's law relates the electric flux through a closed surface to the enclosed charge. Capacitance is the ratio of stored charge on conductors to the potential difference between them.
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole moment, and the electric field intensity and torque experienced by a dipole in a uniform electric field.
This document discusses the concepts of electric fields and electric field intensity. It defines electric field as a region of space around charged particles that exert electrostatic forces on other charges. Electric field intensity is defined as the electrostatic force per unit positive test charge. The electric field due to a point charge is discussed, along with the superposition principle and electric field lines. Electric dipoles are introduced as pairs of equal and opposite charges, with discussions of dipole moment, and the electric field intensity and torque experienced by dipoles.
1. The document provides a refresher on basic differentiation techniques for powers, constants, sums, differences, and other terms.
2. It reviews rules for differentiating simple and general powers, constants, sums and differences of terms, and powers multiplied by constants.
3. Examples and practice problems are provided for each technique to help the reader practice the skills.
This document contains information about different types of waves including mechanical waves, electromagnetic waves, and gravitational waves. It discusses key wave properties such as amplitude, wavelength, frequency, period, and speed. It also covers topics like longitudinal and transverse wave motion, reflection, refraction, and standing waves. Examples are provided to illustrate wave phenomena in various contexts like sound waves, water waves, and seismic waves.
This document discusses concepts related to thermodynamics including:
- Kinetic molecular theory explains heat in terms of molecular motion rather than a fluid called "caloric."
- Internal energy is the sum of kinetic and potential energy of all particles in a substance due to their motion and interactions. Temperature is proportional to average kinetic energy.
- Heat is the transfer of thermal energy between objects of different temperature, while internal energy is the thermal energy contained within an object.
- Thermal equilibrium occurs when objects are at the same temperature so there is no net heat transfer between them. Heat transfer can occur via conduction, convection, or radiation.
Sound waves are longitudinal waves that propagate through a medium by causing oscillations in pressure. The speed of sound depends on properties of the medium like density and bulk modulus. Frequency determines pitch, with the human hearing range from 20-20,000 Hz. The Doppler effect causes changes in observed frequency due to relative motion between source and receiver. Sonar uses echoes to locate objects by sound, while sonic booms occur when the source moves at or faster than the speed of sound.
Optics involves the reflection and refraction of light. Reflection occurs when light bounces off a surface, following the law of reflection where the angle of incidence equals the angle of reflection. Refraction is when light changes speed and direction when passing from one medium to another due to a change in index of refraction. Refraction is described by Snell's law, where the ratio of sines of the incident and refracted angles is equal to the ratio of the indices of refraction. Total internal reflection occurs when light passes from a higher to lower index of refraction beyond the critical angle and is completely reflected rather than refracted.
The magnetic field is weak above the top wire of the current loop because the top and bottom lengths of wire produce magnetic fields in opposite directions (one into the page and one out of the page), which cancel each other out. So at a point directly above the wire, the net magnetic field is small.
Here are the key differences between primary colors in light vs pigments:
- Primary light colors are red, green, and blue. These can be combined to form white light.
- Primary pigment colors are yellow, cyan, and magenta. These absorb one primary light color and reflect the other two.
- Secondary light colors are formed by combining two primary light colors: orange (red + green), violet (red + blue), and yellow (green + blue).
- Secondary pigment colors are formed by absorbing two primary light colors: red (absorbs yellow and cyan), blue (absorbs yellow and magenta), and green (absorbs cyan and magenta).
So in summary, primary
The document discusses several key concepts related to fluids, including:
1) States of matter, phase changes, density, pressure, and Archimedes' principle.
2) Pressure in fluids depends on depth and density, not the shape of the container, according to the formula P=ρgh.
3) Pascal's principle states that pressure changes are transmitted undiminished throughout an enclosed fluid.
This document discusses various topics in electrostatics including:
1) Electric charge can be positive or negative and like charges repel while unlike charges attract.
2) Charge is conserved meaning the total amount of charge in a system remains constant during interactions and transformations.
3) The coulomb is the SI unit for electric charge and small amounts are measured in microcoulombs. The elementary charge is the smallest unit of charge possible.
4) Materials can be conductors, insulators or semiconductors depending on how freely charge can flow through them.
Here are the steps to solve this parallel circuit problem:
1. To find the equivalent resistance Req, use the parallel formula:
1/Req = 1/2.4 + 1/6 + 1/4
1/Req = 0.41667
Req = 2.4 Ω
2. To find the total current Itotal, use Ohm's Law:
V = IReq
15 = 2.4Itotal
Itotal = 6.25 A
3. The voltage across each resistor is 15 V (same in parallel).
Use Ohm's Law to find the current through each:
Imiddle = V/R = 15/6 = 2.5 A
I
1) The document discusses momentum, including its definition as mass times velocity (p=mv), examples of equivalent momenta between objects with different masses and speeds, and the impulse-momentum theorem relating impulse (force times time) to changes in momentum.
2) Conservation of linear momentum is explained, stating that the total momentum of an isolated system is constant. Examples show applying this principle to calculate velocities after collisions.
3) The proof of conservation of momentum relies on Newton's Third Law and the cancellation of internal action-reaction force pairs between objects, leaving the net external force on the overall system as zero.
Newton's Law of Gravitation and Kepler's Laws of Planetary Motion describe gravity and orbital motion. Newton's Law states that the gravitational force between two objects is proportional to their masses and inversely proportional to the square of the distance between them. Kepler's Laws state that planets move in ellipses with the Sun at one focus, sweep out equal areas in equal times, and have periods proportional to the 3/2 power of their distances from the Sun.
The document discusses projectile motion, describing how objects moving through the air are affected by gravity. It explains that gravity only affects vertical motion, not horizontal motion, so horizontally a projectile maintains a constant velocity if no other forces are present. Examples are provided to demonstrate how to calculate the time of flight, range, and landing point of projectiles fired at various angles and velocities.
mg sinθ - μk mg cosθ = ma
So, a = (mg sinθ - μk mg cosθ) / m = g(sinθ - μk cosθ)
The acceleration depends on the angle and the coefficient of
kinetic friction.
This document discusses Newton's laws of motion and provides examples of forces. It introduces Newton's three laws, including inertia, Fnet=ma, and action-reaction. Examples are given for each law such as an astronaut drifting in space (1st law), graphs of force vs. acceleration (2nd law), and collisions between objects of different masses (3rd law). Common forces like gravity, tension, and normal forces are also explained.
This document provides an overview of key physics concepts related to kinematics including:
- Vectors and scalars
- Displacement, distance, velocity, acceleration, and their relationships
- Mass vs weight
- Motion graphs including position, velocity, and acceleration graphs
- Kinematics equations for constant acceleration including relationships between displacement, velocity, acceleration, and time
- Sample kinematics problems and explanations of concepts like uniform acceleration are provided.
1. Electric Fields
• Review of gravitational fields
• Electric field vector
• Electric fields for various charge configurations
• Field strengths for point charges and uniform fields
• Work done by fields & change in potential energy
• Potential & equipotential surfaces
• Capacitors, capacitance, & voltage drops across capacitors
• Millikan oil drop experiment
• Excess Charge Distribution on a Conductor
2. Gravitational Fields: Review
Recall that surrounding any object with mass, or collection of objects with mass, is a
gravitational field. Any mass placed in a gravitational field will experience a
gravitational force. We defined the field strength as the gravitational force per unit
mass on any “test mass” placed in the field: g = F / m. g is a vector that points in
the direction of the net gravitational force; its units are N / kg. F is the vector force
on the test mass, and m is the test mass, a scalar. g and F are always parallel. The
strength of the field is independent of the test mass. For example, near Earth’s
surface mg / m = g = 9.8 N / kg for any mass. Some fields are uniform (parallel,
equally spaced fields lines). Nonuniform fields are stronger where the field lines are
closer together.
uniform field
10 kg
nonuniform
field Earth
98 N
F
m
Earth’s surface
3. Electric Fields: Intro
Surrounding any object with charge, or collection of objects with charge, is a
electric field. Any charge placed in an electric field will experience a electrical
force. We defined the field strength as the electric force per unit charge on any “test
charge” placed in the field: E = F / q. E is a vector that points, by definition, in the
direction of the net electric force on a positive charge; its units are N / C. F is the
vector force on the test charge, and q is the test charge, a scalar. E and F are only
parallel if the test charge is positive. Some fields are uniform (parallel, equally
spaced fields lines) such as the field on the left formed by a sheet of negative charge.
Nonuniform fields are stronger where the field lines are closer together, such as the
field on the right produced by a sphere of negative charge.
uniform field
+q nonuniform
field -
F
F
+
q
--------------
4. Overview of Fields
Charge, like mass, is an intrinsic property of an object. Charges produce electric
fields that affect other charges; masses produce gravitational fields that affect other
masses. Gravitational fields lines always point toward an isolated mass. Unlike
mass, though, charges can be positive or negative. Electric field lines emanate from
positive charges and penetrate into negative charge.
We refer to the charge producing a field as a field charge. A group of field charges
can produce very nonuniform fields. To determine the strength of the field at a
particular point, we place a small, positive test charge in the field. We then
measure the electric force on it and divide by the test charge: / q.
E=F
For an isolated positive field charge, the field lines point away from the field
charge (since the force on a positive charge would be away from the field charge).
The opposite is true for an isolated negative field charge. No matter how complex
the field, the electric force on a test charge is always tangent to the field line at that
point.
The coming slides will reiterate these ideas and provide examples.
5. Electric & Gravitational Fields Compared
Field Intrinsic
Force SI units
strength Property
Gravity: g = W / m N / kg
Electric
Force: E = FE / q N/C
Field strength is given by per unit mass or force per unit charge,
depending on the type of field. Field strength means the magnitude of a
field vector. Ex #1: If a +10 C charge is placed in an electric field and
experiences a 50 N force, the field strength at the location of the charge is
5 N/C. The electric field vector is given by: E = 5 N/C, where the
direction of this vector is parallel to the force vector (and the field lines).
Ex #2: If a -10 C charge experiences a 50 N force, E = 5 N/C in a
direction opposite the force vector (opposite the direction of the field
lines).
6. Electric Field Example Problem
A sphere of mass 1.3 grams is charged via friction, and in the
process excess electrons are rubbed onto it, giving the sphere a
charge of - 4.8 μC. The sphere is then placed into an external
uniform electric field of 6 N/C directed to the right. The sphere is
released from rest. What is its displacement after 15 s? (Hints on
next slide.)
E
-
7. E
Sample Problem Hints
1. Draw a vector as shown. Note that
FE = q E, by definition of E, and qE -
that FE is to the left (opposite E )
since the charge is negative.
mg
2. Instead of finding the net force
(which would work), compute the
acceleration due to each force
separately.
3. Find the displacement due to each force using the time given and
kinematics.
4. Add the displacement vectors to find the net displacement
vector.
8. Drawing an E Field for a Point Charge
Let’s use the idea of a test charge to produce the E field for an isolated positive field
charge. We place small, positive test charges in the vicinity of the field and draw the
force vector on each. Note that the closer the test charge is to the field charge, the
greater the force, but all force vectors are directed radially outward from the field
charge. At any point near the field charge, the force vector points in the direction of
the electric field. Thus we have a field that looks like a sea urchin, with field lines
radiating outward from the field charge to infinity in all direction, not just in a plane.
The number of field lines drawn in arbitrary, but they should be evenly spaced around
the field charge. What if the field charge were negative?
+ +
Test charges and force vectors Isolated, positive point
surrounding a field charge charge and its electric field
9. Single Positive Field Charge
This is a 2D picture
of the field lines that
surround a positive The nearer you
field charge that is get to the
either point-like or charge, the
spherically more uniform
symmetric. Not and stronger
shown are field lines the field.
going out of and into
Farther away
+
the page. Keep in
mind that the field the field
lines radiate strength gets
outwards because, weaker, as
by definition, an indicated by
electric field vector the field lines
points in the becoming
direction of the force more spread
on a positive test out.
charge.
10. Single Negative Field Charge
The field surrounding an
isolated, negative point (or
spherically symmetric)
charge looks just like that of
an isolated positive charge
except the field lines are
directed toward the field
charge. This is because, by
definition, an electric field
vector points in the direction
of the force on a positive test
-
charge, which, in this case is
toward the field charge. As
before, the field is stronger
where the field lines are
closer together, and the force
vector on a test charge is
parallel to the field.
11. Point Charges of Different Magnitudes
Let’s compare the fields on two separate isolated point charges, one with a
charge of +1 unit, the other with a charge of +2 units. It doesn’t matter how
many field lines we draw emanating from the +1 charge so long as we draw
twice as many line coming from the +2 charge. This means, at a given
distance, the strength of the E field for the +2 charge is twice that for the +1
charge.
+1 +2
12. Equal but Opposite Field Charges
Pictured is the electric field produced by two equal but opposite
charges. Because the charges are of the same magnitude, the field is
symmetric. Note that all the lines that emanate from the positive
charge land on the negative charge. Also pictured is a small positive
charge placed in the field and the force vector on it at that position.
This is the vector sum of the forces exerted on the test charge by each
field charge. Note that the net force vector is tangent to the field line.
This is always the case. In fact, the field is defined by the direction of
net force vectors on test charges at
various places. The net force on a
negative test charge is tangent to the
field as well, but it points in the +
opposite direction of the field.
(Continued on next slide.) -
Link #1 Link #2 Link #3
13. Equal but Opposite Field Charges (cont.)
D
C
- +
A
B
Here is another view of the field. Since the net force on a charge can only be
in one direction, field lines never intersect. Draw the electric force on a
positive charge at A, the electric field vector and B, and the electric force on a
negative charge at C. The net force on a + charge at D charge is directly to the
left. Show why this is the case by drawing force vectors from each field
charge and then summing these vectors.
14. Multiple Charges: How to Determine the Field
To determine the field surrounding two field charges, Q 1 and Q2, we pick
some points in the vicinity and place test charges there (red dots). Q 1
exerts a force on each, directly away from itself (blue vectors), as does
Q2 (purple vectors). The resultant vectors (black) show the direction of
the net electric force and define the direction of the electric field.
The net force vector on each test
charge is tangent to the E field
there. If we place little a tangent
segment parallel with the net
force at each test charge and do Q2
this at many different points, we Q1 + +
will build a picture of the electric
field. The same procedure can be
used regardless of the number of
field charges.
15. Two Identical Charges
+ +
With two identical field charges, the field is symmetric but all field
lines go to infinity (if the charges are positive) or come from infinity (if
the charges are negative). As with any field the net force on a test
charge is tangent to the field. Here, each field charge repels a positive
test charge. The forces are shown as well as the resultant vectors, which
are tangent to the field lines.
16. Coulomb’s Law Review
The force that two point charges, Q and q, separated by a distance r,
exert on one another is given by:
KQq where K = 9 × 109 Nm2/C2 (constant).
F= 2
r
This formula only applies to point charges or spherically
symmetric charges.
Suppose that the force two point charges are exerting on one
another is F. What is the force when one charge is tripled, the
other is doubled, and the distance is cut in half ?
Answer: 24 F
17. Field Strengths: Point Charge; Point Mass
Suppose a test charge q is placed in the electric field produced by a
point-like field charge Q. From the definition of electric field and
Coulomb’s law
F K Q q / r2 KQ
E= = = 2
q q r
Note that the field strength is independent of the charge placed in it.
Suppose a test mass m is placed in the gravitational field produced
by a point-like field mass M. From the definition of gravitational
field and Newton’s law of universal gravitation
F G M m / r2 GM
g= = = 2
m m r
Again, the field strength is independent of the mass place in it.
18. Uniform Field
Just as near Earth’s surface the gravitational field is approximately
uniform, the electric field near the surface of a charged sphere is
approximately uniform. A common way to produce a uniform E field is
with a parallel plate capacitor: two flat, metal, parallel plates, one
negative, one positive. Aside from some fringing on the edges, the field
is nearly uniform inside. This means everywhere inside the capacitor the
field has about the same magnitude and direction. Two positive test
charges are depicted along with force vectors.
- - - - - - - -
+ + + + + + + +
19. Two + Field Charges of Different Magnitude
• More field lines emanate from the greater charge; none of the
field lines cross and they all go to infinity.
• The field lines of the greater charge looks more like that of an
isolated charge, since it dominates the smaller charge.
• If you “zoomed out” on this picture, i.e., if you looked at the
field from a great distance, it would look like that of an
isolated point charge due to one combined charge.
Although in this pic the
greater charge is depicted as
+ + physically bigger, this need
not be the case.
20. Opposite Signs, Unequal Charges
The positive charge has a greater magnitude than the negative charge.
Explain why the field is as shown. (Answer on next slide.)
+ -
21. Opposite Signs, Unequal Charges (cont.)
+ -
More field lines come from the positive charge than land on the negative.
Those that don’t land on the negative charge go to infinity. As always, net
force on a test charge is the vector sum of the two forces and it’s tangent to the
field. Since the positive charge has greater magnitude, it dominates the
negative charge, forcing the “turning points” of the point to be closer to the
negative charge. If you were to “zoom out” (observe the field from a distance)
it would look like that of an isolated, positive point with a charge equal to the
net charge of the system.
22. Summary of Fields due to Unequal Charges
You should be able to explain each case in some detail.
23. Review of Induction
Valence electrons of a conductor
are mobile. Thus they can
respond to an electric force from
a charged object. This is called
charging by induction. Note: not
all of the valence electrons will
move from the bottom to the top.
+
The greater the positive charge
brought near it, and the nearer it
is brought, the more electrons that
will migrate toward it. (See
animation on next slide.) + - + - + - +- +
conductor
+ - + - + - +-+
24. Review of Induction (cont.)
Because of the
displaced electrons, a
+ charge separation is
induced in the
conductor.
+ - + - + - + -+ -
+ - + - + - + - +-
25. Positive Charge Near a Neutral Conductor
• The + charge induces a
charge separation on the
neutral conductor.
• Since it is neutral, as many
+ lines land on the conductor as
leave it.
• The number of field lines that
- go off to infinity is the same
+ as if the + charge were
isolated.
• Viewed from afar, the field
would look like that of an
26. Overview of Field Types
For the following scenarios, you should be able to draw the
associated electric fields correctly:
1. A uniform field
2. An isolated + point charge
3. An isolated – charge
4. Two identical + point charges
5. Two identical – point charges
6. Point charge (either sign) near neutral
conductor
7. Unequal point charges of the same sign
8. Unequal point charges of the opposite sign
Note that a field drawn without a direction indicated (without arrows)
is incorrect. You should be able to draw vector forces on positive or
negative charges placed in any field. Also, for complex fields you
should be able to describe them as the appear from a distance.
27. Work done by Fields & Applied Forces
To lift an object of mass m a height h in a uniform gravitational field
g without acceleration, you must apply a force m g. The work you do
is + m g h, while the work done by the field is - m g h. When you lower
the object, you do negative work and the field does positive work.
Near the surface of a negatively charged object, the electric field is
nearly uniform. To lift without acceleration a positive charge q in a
downward field E requires a force q E. You do positive work in lifting
the charge, and the field does negative work. The signs reverse when
you lower the charge.
m g E +q
mg qE
Earth’s surface Negatively charged surface
28. Fields: Work & Potential Energy
The work your applied force does on the mass or on the charge can go into
kinetic energy, waste heat, or potential energy. If there is no friction and no
acceleration, then the work you do goes into a change of potential energy:
∆U = m g ∆h for a mass in a gravitational field and ∆U = q E ∆h for a
charge in a uniform electric field. The sign of ∆h determines the sign of
∆U. (If a charged object is moved in a vicinity where both types of fields
are present, we’d have to use both formulae.) Whether or not there is
friction or acceleration, it is always the case that the work done by the field
is the opposite of the change in potential energy: Wfield = - ∆U.
m g E +q
mg qE
Earth’s surface Negatively charged surface
29. Work-Energy Example
Here the E field is to the right and approximately uniform. The applied
force is FA to the left, as is the displacement.
The work done by FA is + FA d.
The work done by the field is WF = - q E d.
The change in electric potential energy is ∆U = - WF = + q E d.
Since FA > q E, the applied force does more positive work than the field
does negative work. The difference goes into kinetic energy and heat.
The work done by friction is Wfric < 0. So, Wnet = FA d - q E d - |Wfric|
= ∆K by the work-energy theorem.
+ d -
+ -
+ FA qE -
+ + -
q
+ -
30. Work-Energy Practice
For each situation a charge is displaced by some applied force while
in a uniform electric field. Determine the sign of: the work done by
the applied force; the work done by the field; and ∆U.
1. q is positive and displaced to the right.
2. q is negative and displaced to the right.
3. q is positive and displaced to the left.
4. q is negative and displaced to the left.
+ -
+ -
+ q -
+ -
+ -
31. Potential
Gravitational potential is defined to be gravitational potential energy per unit
mass. At any given height above Earth’s surface, the gravitational potential is
a constant since U / m = m g h / m = g h. Thus potential is independent of
mass. If M > m and they’re at the same height, M has more potential energy
than m, but they are at the same potential.
Similarly, electric potential, V, is defined to be electric potential energy per
unit charge. At any given distance from a charged surface in a uniform field,
the electric potential is a constant since U / q = q E d / q = E d. Thus potential
is independent of charge. If Q > q and they’re the same distance from the
surface, Q has more potential energy than q, but they are at the same
potential. In a uniform field V = E d.
g E
m M
q Q
h d
Earth’s surface Negatively charged surface
32. SI Units for Potential
By definition, electric potential is potential energy per unit charge. So,
U
V= q
The SI unit for electric potential is the volts. Both potential and its
unit are notated by the capital letter “V.” Based on the definition
above, a volt is defined as joule per coulomb:
1J
1V=
C
Ex: If an object with a 10 C charge is placed at a certain point in an
electric field so that its potential energy is 50 J, every coulomb of
charge in the object contributes to 5 J of its energy, and its potential is
5 J / C, that is, 5 V.
33. Equipotential Surfaces
As with gravitational potential energy, the reference point for electric potential energy,
and hence potential, is arbitrary. Usually what matters is a change in potential, so we
just pick a convenient place to call potential energy zero. The dotted lines on the left
represent equipotential surfaces--planes in which masses all have the same potential,
regardless of the mass. On the 30 J/kg surface, for example, every kilogram of every
mass has 30 J of potential energy. Note that equipotentials are always perpendicular to
field lines.
The equipotentials on the right are labeled in volts. Potential decreases with distance
from a positively charged surface since a positive charge loses potential energy as it
recedes from the surface. Here again the equipotentials are perpendicular to the field
lines. On the -45 V surface, every coulomb of charges has -45 J of potential energy.
A -2 C charge there has a potential energy of +90 J.
40 J / kg -60 V
30 J / kg -45 V
20 J / kg -30 V
10 J / kg -15 V
0 J / kg 0V
Earth’s surface Positively charged surface
34. Contour Map Analogy
Earth’s gravitational field doesn’t diminish much over the height of a mountain, so
the field is nearly uniform and the equipotentials are evenly spaced, parallel planes.
Thus the dotted lines are equally spaced (side view). As seen from above, though, the
corresponding contour lines are not equally spaced. They are closer together where
the potential energy changes rapidly (steep part of the mountain), and they’re far
apart where the energy changes gradually (gentle sloping part of mountain). Contour
lines connect points of equal elevation, so walking along one mean your potential
energy remains constant. They are analogous to equipotentials.
top view
side view
steep
not steep
35. Equipotential Surfaces: Positive Point Charge
Imagine a positive test charge, q, approaching an isolated, positive, point-
like field charge, Q. The closer q approaches, the more potential energy it
has. So, potential increases as distance decreases. Next year we’ll derive this
formula for potential due to a point charge: V = KQ / r. This shows that V is
proportional to Q, that V → 0 as r → ∞, and that V → ∞ as r → 0.
Equipotential surfaces are always perpendicular to the field lines, for any
charge configuration. For a point charge the
surfaces are spheres centered at Q.
Here the surfaces could be labeled from
the inside out: 100V, 90 V,
80 V, and 70 V. Every 10 V step is
bigger than the previous, since the field
is getting weaker with distance. The +
gap between the 50 V and 40 V
surfaces would be very large, and the
gap between 10 V and 0 V would be
infinite.
36. Equipotential Surfaces: Negative Point Charge
The field and the equipotentials look just like that of the isolated,
positive point charge. However, the field lines point in the opposite
direction and the potential decreases with distance. Imagine a positive
test charge, q, approaching an isolated, negative, point-like field
charge, -Q. The closer q approaches, the more negative its potential
energy becomes. So, V → 0 as r → ∞ (as with the positive field
charge), but V → - ∞ as r → 0.
Here the surfaces could be labeled
from the inside out: -100V, -90 V,
-80 V, and -70 V. Every 10 V step
is bigger than the previous, since
V = zero at infinity. (The step size -
to be drawn is a matter of choice.)
A +3 C charge placed on the -70 V
surface has a potential energy of
-210 J.
37. Equipotentials Surfaces for Multiple-charge Configurations
In class practice: First experiment with the link, then draw equipotentials
on the board on top of this picture. Here are the rules:
• Equipotentials are always
Link
perpendicular to the field lines.
• Equipotentials never intersect
one another.
• The potential is large &
positive near a positive charge, +
large & negative near a
negative charge, and near
zero far from all the charges.
-
• Equipotentials are close
together where potential
energy changes quickly
(close to charges).
38. Moving in an Electric Field
Electric and gravitation fields are called conservative fields because, when
a mass/charge moves about one, any change in potential energy is
independent of path. A charge taking a straight-line path from A to B
undergoes a change in potential of 10 V (∆V = +10 V). If a charge takes the
long, curvy path, its energy increases as
it approaches the field charge, and
decreases as it recedes, but the change D
is the same as the straight-line path.
In either case each coulomb of C
charge gains 10 J of potential energy.
A B
No matter what path is taken:
∆VC→A = -20 V, and ∆VD→A = 0.
+
10
∆V is independent of path!
0
90
From A to D along the equipotential the
V
V
field can do no work, since the 80
displacement if always to E, which is V
70
|| to F. Recall: W = F · x = F x cosθ.
V
39. Capacitors - Overview
• A capacitor is a device that stores electrical charge.
• A charged capacitor is actually neutral overall, but it maintains
a charge separation.
• The charge storing capacity of a capacitor is called its
capacitance.
• An electric field exists inside a charged capacitor, between the
positive and negative charge separation.
• A charged capacitor store electrical potential energy.
• Capacitors are ubiquitous in electrical devices. They’re used in
power transmission, computer memory, photoflash units in
cameras, tuners for radios and TV’s, defibrillators, etc.
40. capacitor
Parallel Plate Capacitor
The simplest type of capacitor is a
parallel plate capacitor, which consists -Q +Q
of two parallel metal plates, each of Area, A
area A, separated by a distance d. When
one plate is attached via a wire to the + d
terminal of a battery, and the other plate
is connected to the - terminal, the
battery pulls e-’s from the plate V
connected to the - terminal and wire
battery
deposits them on the other. As a whole
the capacitor remains neutral, but we say it now has a C
charge Q, the amount of charge moved from one plate to
the other. Without a resistor in the circuit, the capacitor
charges very quickly. Thus the current, i, which by +Q -Q
definition is in the opposite direction of the flow of e -’s,
lasts but a short time. As soon as the voltage drop across the
capacitor (the potential difference between its plates) is the
i
same as that of the battery, V, the charging ceases. The V
capacitor can remain charged even when disconnected from
the battery. Note the symbols used in the circuit diagram to
41. Parallel Plate Capacitor: E & U
Because of the charge separation, an electric field exists between the plates of a
charged capacitor. If it is a parallel plate variety, the field is very nearly uniform
inside, with some fringing on the edges, as we’ve seen before. Outside the plates the
field is very weak. The strength of the E field inside is proportional to how much
charge is on the capacitor and inversely proportional to how the capacitors area. (Less
area means the charge is more concentrated and the field is stronger.) A charged
capacitor also stores potential energy (in an amount proportional to the square of the
charge) since energy is required to separate the charges in the first place. Touching a
charged capacitor will allow it to discharge quickly and will result in a shock. Once
discharged, the electric field vanishes and the potential energy is converted to some
other form.
- - - - - - - -
+ + + + + + + +
42. Capacitance
Capacitance, C, is the capacity to store charge. The amount of charge,
Q, stored on given capacitor depends on the potential difference
between its plates, V, and its capacitance C. In other words, Q is
directly proportional to V, and the constant of proportionality is C:
Q = CV
Ex: A 12 V battery will cause a capacitor to store
twice as much charge as a 6 V battery. Also, if C
capacitor #2 has twice the capacitance of capacitor
#1, then #2 will store twice as much charge as #1,
provided they are charged by the same battery. Q
C depends on the type of the capacitor. For a
parallel plate capacitor, C is proportional to the
V
area, A and inversely proportional to the plate
separation, d.
43. Capacitance: SI Units
The SI unit for capacitance is the farad, named for the famous
19th century scientist Michael Faraday. Its symbol is F. From the
defining equation for capacitance, Q = CV, we define a farad:
Q = CV
implies 1 C = (1 F) (1 V)
So, a farad is a coulomb per volt. This means a capacitor with a
capacitance of 3 F could store 30 C of charge if connected to a 10 V
battery. This is a tremendous amount of charge for a reasonable
potential difference. Thus a farad is a large amount of capacitance.
Many capacitors have capacitances measured in pF or fF (pico or
femtofarads).
m: milli = 10-3, μ: micro = 10-6, n: nano = 10-9,
p: pico = 10-12, f: femto = 10-15
44. Capacitance Problem
A parallel plate capacitor is fully charged by a 20 V battery, acquiring
a charge of 1.62 nC. The area of each plate is 3.5 cm2 and the gap
between them is 1.3 mm. What is the capacitance of the capacitor?
From Q = C V, C = Q / V = (1.62 × 10-9 C) / (20 V)
= 8.1 × 10-11 F = 81 × 10-12 F = 81 pF.
The gap and area are extraneous.
- 1.62 μC
+ 1.62 μC
3.5 cm2
1.3 mm
20 V
45. V = Ed
As argued on the slide entitled “Potential,” in a uniform field,
V = E d. This argument was based on an analogy with gravity and
applies only to uniform fields:
gravitational: U = m g h
electric: U = q E d ⇒ U / q = E d ⇒ V = E d
Since E is uniform inside a parallel plate capacitor, the voltage drop
across it is equal to the magnitude of the electric field times the
distance between the plates.
d
46. V = E d (formal derivation)
U (from the definition of potential)
V=
q
|Wfield | (since Wfield = - ∆U )
V=
q
Fd (since W = F d )
V=
q
F
∆V= E d (since E = )
q
47. Millikan’s Oil Drop Experiment
In 1909, Robert Millikan performed an experiment to determine the
charge of an electron. The charge to mass ratio of the electron had
already been calculated by J. J. Thomson (discoverer of the electron) in
1897. But until Millikan’s experiment, neither the mass nor the charge
was known, only the ratio. By examining the motion of the oil droplets
falling between two highly charged plates, he found the charge to be
-1.6 ×10-19 C. The charged plates were similar to that of a parallel plate
capacitor.
48. Millikan Apparatus and
Experiment
A battery connected to the plates kept the top (positive) plate at a higher
potential than the lower (negative) plate. So, a nearly uniform, downward E
field existed between the plates. An atomizer sprayed tiny oil droplets (of radii
about 1 μm) from above the plates, some of which fell through a hole in the
positive plate into the E field. Due to friction during the spraying, some of
the drops were charged, either positively or negatively. A negatively charged
drop that makes it into the hole will not undergo free fall, since it experiences
an upward electric force between the plates. The radius, mass, and charge of
the drops varied, but by adjusting the potential difference across the plates,
Millikan could make a drop hover. Continued…
switch
49. Oil Drop Experiment (cont.)
A drop suspended in midair has no net force on it. This means the downward
weight, m g, was negated by an upward electric force, q E. Millikan could
vary E by adjusting the potential difference across the plates (V = E d). So,
the excess charge on the drop is: q = m g / E = m g d / V.
But m needed to be calculated in order to determine q.
To find the drop’s mass, he turned off the electric field by opening the switch
and disconnecting the battery. The drop then began to fall, but it quickly
reached terminal velocity in the air. The greater the falling speed, the greater
the drag force, and by measuring terminal speeds, Millikan could calculate the
mass. Continued…
qE
switch
- d
mg
50. Oil Drop Experiment (cont.)
At this point Millikan could calculate the charge on a drop. But without
knowing the number of excess electrons on the drop, he couldn’t determine
the charge of an electron. So, he altered the charge on the drop with X-rays
(not shown). The X-rays ionized the surrounding air, which, in turn, altered
the charge on the drops. The drops were now no longer in equilibrium, so
Millikan adjusted the E field until equilibrium was reestablished.
Since at equilibrium q = mgd / V, and all quantities on the right side of the
equation were known, Millikan could repeat this X-ray procedure numerous
times and calculate the many different charges that a drop could attain. He
found that the charge on a drop was always a multiple of 1.6 × 10-19 C. As
you know, we now call this amount of charge e, the elementary charge.
His experiment showed that charge is quantized, existing in discrete bundles
(in this case, electrons) and that the charge on an electron is -1.6 × 10-19 C.
51. Excess Charge on a Conductor
Any excess charge placed on a conductor will immediately distribute itself
over the surface of the conductor. No excess charge will remain inside. On
a spherical conductor the excess charge will be distributed evenly. If
electrons are added, they themselves will spread out. If electrons are
removed, electrons in the conductor will replace them, leaving all excess
positive charge on the surface. Excess charge placed on an insulator pretty
much stays put.
Now lets add some extra
_ _ charges.
+ + _
_
_ _
_ _
+ + _ The new charges repel
_ + themselves and reside only on
+ the surface.
52. Excess Charge on a Pointy Conductor
Excess charge, which always resides on the surface of a conductor, will collect in
high concentrations at points. In general, the smaller the radius of curvature, R, the
greater the charge density (charge per unit area). The reason for this is that when
R is large, neighboring charges push a charge nearly tangent to the surface (left
pic). But where R is small (as near a point), neighboring charges are mostly
pushing a charge outward, away from the surface instead of away from each other
(right pic). This allows the charges be reside closer together.
vector forces due to neighboring charges
_ _ ____
_ __
_
_ _ _
_ small R, high
_ _ charge density _ _
_ _ _ _
_ _ _ large R, low _
_ _ _ charge density _
_ _ _ _
_ _ _
_ _ _ _
_ _ _
uniform R, uniform charge density
53. Electric Fields In & Around Charged Conductors
E is always zero inside any conductor, even a charged one. If this were not
the case, mobile valence electrons inside the conductor would be
accelerated by the E field, leaving them in a state of perpetual motion.
Outside a charged conductor E is greater where the charge density is
greater. Near points, E can be extremely high. Surrounding a sphere the
field is radially symmetric, just the field due to a point charge.
____
_ __
_
_ _ _ small R, _
_ _ strong E _ _
_ _
_ _ _ _
E=0 _ _ E=0 _
_ _ _
_ inside _ _ inside _
_ _ _ _
_
_ _ _ large R, _ _ _
_
weak E
E is radially symmetric outside.
54. Shielding Electric Fields
A box or room made of metal or with a metal liner can shield its
interior from external electric fields. Valence e-’s in the metal will
respond to the field and reorient themselves until the field inside
the box no longer exists. The external field (black) points right.
This causes a charge separation in the box (e-’s migrating left),
which produces its own field (red), negating the external field.
Thus, the net field inside is zero. Outside, the field persists.
- +
- +
- +
- +
55. Credits
http://images.google.com/imgres?
imgurl=http://buphy.bu.edu/~duffy/PY106/2e.GIF&imgrefurl=http://physics.bu.edu/~duffy/PY106/Electricfield.html
&h=221&w=370&sz=4&tbnid=y0qny4b133kJ:&tbnh=70&tbnw=117&start=3&prev=/images%3Fq%3Delectric
%2Bfield%26hl%3Den%26lr%3D
Spark Picture: http://cdcollura.tripod.com/tcspark2.htm
electric field lines: http://www.gel.ulaval.ca/~mbusque/elec/main_e.html
java, placing and moving test charges and regular charges:
http://www.physicslessons.com/exp21b.htm
java animation, placing test charges:
http://www.colorado.edu/physics/2000/waves_particles/wavpart3.html
http://www.slcc.edu/schools/hum_sci/physics/tutor/2220/e_fields/
lesson, pictures, units: http://www.pa.msu.edu/courses/1997spring/PHY232/lectures/efields/
java electric field: http://www.msu.edu/user/brechtjo/physics/eField/eField.html
lesson with animations, explanations: http://www.cyberclassrooms.net/~pschweiger/field.html
http://library.thinkquest.org/10796/ch12/ch12.htm
Robert Millikan: http://www.nobel.se/physics/laureates/1923/millikan-bio.html
Millikan Oil Drop: http://www.mdclearhills.ab.ca/millikan/experiment.html
http://www.glenbrook.k12.il.us/gbssci/phys/Class/estatics/u8l4c16.gif
http://www.physchem.co.za/Static%20Electricity/Graphics/GRDA0008.gif
http://www.eng.uct.ac.za/~victor/electric/charge_opposite_particles.gif