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) Coulomb's Law describes the electrostatic force between two charged objects, which depends on the magnitude and type of their charges and the distance between them.
2) The electrostatic force follows an inverse square relationship with distance, similar to Newton's Law of Gravitation. However, electrostatic force concerns charge while gravitational force concerns mass.
3) For small charged objects like electrons and protons, the electrostatic force is much stronger than the gravitational force due to their small size.
The document describes the concept of diffraction of waves. It discusses how diffraction causes waves to bend or spread out when passing through an obstacle or gap. It provides examples of diffraction of water waves and discusses how the degree of diffraction depends on factors like the size of the obstacle or gap relative to the wavelength. The document also discusses how diffraction causes the shape, direction and amplitude of waves to change while keeping the wavelength and frequency the same. It poses sample questions assessing understanding of diffraction concepts.
The document discusses concepts related to electric charge, electric fields, and electric circuits. Some key points covered include:
- Charged objects exert forces on each other via an electric field according to Coulomb's law. The electric field is defined as the force per unit charge.
- Conductors allow free flow of electric charge while insulators do not. Resistors in circuits control current flow according to Ohm's law.
- Electric potential energy and voltage difference can be defined from the work done in electric fields. Equipotential surfaces exist where electric potential is constant.
- Electric current is the rate of flow of electric charge through a cross-sectional area of a conductor. Current, voltage, and resistance
This document discusses transverse wave motion. It defines transverse waves as disturbances that occur perpendicular to the direction of propagation. Transverse waves include electromagnetic waves and waves on strings. The document covers characteristics of waves like wavelength and frequency. It derives the one-dimensional wave equation and explores solutions and properties of transverse waves, including phase velocity, group velocity, and impedance. Key concepts covered are the definitions of progressive and standing waves, and the distinction between particle/oscillator velocity and wave/phase velocity.
1. This document covers key concepts in ray optics including refraction through a prism, dispersion, compound microscopes, astronomical telescopes, and resolving power. It defines terms like refractive index, angle of deviation, angular dispersion, and dispersive power.
2. Refraction through a prism is analyzed using Snell's law. The angle of deviation depends on the angle of incidence and reaches a minimum value. Prism dispersion is explained by wavelengths refracting at different angles according to their frequency.
3. Compound microscopes use two converging lenses, an objective and eyepiece, to magnify images. Angular magnification is calculated using lens equations and depends on focal lengths and distances. Telescopes
ELECTROSTATICS:Coulomb's law, Electric field & problemsDr.SHANTHI K.G
This document provides an overview of the topics covered in the unit on electrostatics, including:
- Coulomb's law, electric fields, Gauss's law and applications.
- Electric potential, conductors and dielectrics in static electric fields.
- Boundary conditions and capacitance of parallel, cylindrical, and spherical capacitors.
- Electrostatic energy and Poisson's and Laplace's equations.
- Current density, Ohm's law, electromotive force, and Kirchhoff's laws.
It then goes on to define Coulomb's law, the electric field intensity, and the principle of superposition. Examples of calculating electric force and field due to point charges are also provided
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as electric fields, magnetic fields, and light, and is one of the four fundamental interactions (commonly called forces) in nature. The other three fundamental interactions are the strong interaction, the weak interaction, and gravitation.[1] At high energy the weak force and electromagnetic force are unified as a single electroweak force.
1. The document discusses electrostatic force and electric charge. It explains that when certain materials are rubbed together, they acquire a property called electricity that allows them to attract small pieces of paper.
2. Electric charge is a property of objects that causes electrical and electromagnetic effects. Charge can be positive, negative, or neutral. Charge is quantized and can only occur in discrete integer multiples of the elementary charge.
3. An electric field is the region of space around a charged object where other charged objects will feel an electrostatic force. The electric field strength is defined as the force on a small test charge placed in the field.
1) Coulomb's Law describes the electrostatic force between two charged objects, which depends on the magnitude and type of their charges and the distance between them.
2) The electrostatic force follows an inverse square relationship with distance, similar to Newton's Law of Gravitation. However, electrostatic force concerns charge while gravitational force concerns mass.
3) For small charged objects like electrons and protons, the electrostatic force is much stronger than the gravitational force due to their small size.
The document describes the concept of diffraction of waves. It discusses how diffraction causes waves to bend or spread out when passing through an obstacle or gap. It provides examples of diffraction of water waves and discusses how the degree of diffraction depends on factors like the size of the obstacle or gap relative to the wavelength. The document also discusses how diffraction causes the shape, direction and amplitude of waves to change while keeping the wavelength and frequency the same. It poses sample questions assessing understanding of diffraction concepts.
The document discusses concepts related to electric charge, electric fields, and electric circuits. Some key points covered include:
- Charged objects exert forces on each other via an electric field according to Coulomb's law. The electric field is defined as the force per unit charge.
- Conductors allow free flow of electric charge while insulators do not. Resistors in circuits control current flow according to Ohm's law.
- Electric potential energy and voltage difference can be defined from the work done in electric fields. Equipotential surfaces exist where electric potential is constant.
- Electric current is the rate of flow of electric charge through a cross-sectional area of a conductor. Current, voltage, and resistance
This document discusses transverse wave motion. It defines transverse waves as disturbances that occur perpendicular to the direction of propagation. Transverse waves include electromagnetic waves and waves on strings. The document covers characteristics of waves like wavelength and frequency. It derives the one-dimensional wave equation and explores solutions and properties of transverse waves, including phase velocity, group velocity, and impedance. Key concepts covered are the definitions of progressive and standing waves, and the distinction between particle/oscillator velocity and wave/phase velocity.
1. This document covers key concepts in ray optics including refraction through a prism, dispersion, compound microscopes, astronomical telescopes, and resolving power. It defines terms like refractive index, angle of deviation, angular dispersion, and dispersive power.
2. Refraction through a prism is analyzed using Snell's law. The angle of deviation depends on the angle of incidence and reaches a minimum value. Prism dispersion is explained by wavelengths refracting at different angles according to their frequency.
3. Compound microscopes use two converging lenses, an objective and eyepiece, to magnify images. Angular magnification is calculated using lens equations and depends on focal lengths and distances. Telescopes
ELECTROSTATICS:Coulomb's law, Electric field & problemsDr.SHANTHI K.G
This document provides an overview of the topics covered in the unit on electrostatics, including:
- Coulomb's law, electric fields, Gauss's law and applications.
- Electric potential, conductors and dielectrics in static electric fields.
- Boundary conditions and capacitance of parallel, cylindrical, and spherical capacitors.
- Electrostatic energy and Poisson's and Laplace's equations.
- Current density, Ohm's law, electromotive force, and Kirchhoff's laws.
It then goes on to define Coulomb's law, the electric field intensity, and the principle of superposition. Examples of calculating electric force and field due to point charges are also provided
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as electric fields, magnetic fields, and light, and is one of the four fundamental interactions (commonly called forces) in nature. The other three fundamental interactions are the strong interaction, the weak interaction, and gravitation.[1] At high energy the weak force and electromagnetic force are unified as a single electroweak force.
1. The document discusses electrostatic force and electric charge. It explains that when certain materials are rubbed together, they acquire a property called electricity that allows them to attract small pieces of paper.
2. Electric charge is a property of objects that causes electrical and electromagnetic effects. Charge can be positive, negative, or neutral. Charge is quantized and can only occur in discrete integer multiples of the elementary charge.
3. An electric field is the region of space around a charged object where other charged objects will feel an electrostatic force. The electric field strength is defined as the force on a small test charge placed in the field.
1. Waves transfer energy from one place to another through a medium without transferring matter. They are produced by a vibrating or oscillating source and can be transverse or longitudinal.
2. Key wave properties include amplitude, wavelength, period, frequency, and speed. Amplitude is the maximum displacement from equilibrium, wavelength is the distance between peaks, period is time for one cycle, frequency is cycles per second, and speed depends on wavelength and frequency.
3. Waves can be characterized by displacement-time graphs showing oscillation over time or displacement-distance graphs showing the pattern of compression and rarefaction as the wave propagates through a medium.
Electricity is created by the interaction of positive protons and negative electrons. Electrons are attracted to protons, forming ions, and can move between atoms. Objects become electrically charged through friction, contact with another charged object, or induction, which is the redistribution of electrons. Electrical conductors like metals allow electron movement, while insulators do not. Electrical force follows Coulomb's law and is measured in volts. Electric current is the flow of electric charge through a conductor. Resistance opposes current and is measured in ohms according to Ohm's law. Electrical circuits use a voltage source to power devices by transferring energy.
Static electricity is a stationary electric charge built up on the surface of materials. It is caused by electrons being transferred between two objects during friction. There are two types of charges - positive and negative. Atoms contain protons which have a positive charge and electrons which have a negative charge. The laws of electrostatics state that like charges repel and unlike charges attract. Materials that allow charge to pass through are conductors, while insulators do not. When a charged object is brought near an uncharged object, the electric field can induce charges in the uncharged object. Some applications of static electricity include electrostatic precipitators, printers, and photocopiers. Grounding neutralizes charged objects by connecting them to the earth.
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.
In this relative motion and relative speed concept is demonstrated with help of examples, graphically and mathematically. The concepts of Einstein and Galileo
1. Electrostatics involves electric charges at rest, which arise from the particles that make up atoms. Atoms have equal numbers of protons and electrons, giving them a net neutral charge.
2. Objects can become charged through friction, induction, or conduction. Friction charging involves the transfer of electrons between two objects in contact. Induction charging uses a charged object to polarize a neutral object without direct contact.
3. The amount and type of charge on an object depends on whether it has an excess or deficit of electrons compared to protons. Coulomb's law describes the relationship between charged objects based on their relative charges and distance.
1. This document discusses several topics related to electricity including Kirchhoff's laws, Wheatstone bridge, metre bridge, and potentiometer.
2. Kirchhoff's laws include the junction rule which states the algebraic sum of currents at a junction is zero, and the loop rule which states the algebraic sum of potential drops around any closed loop is zero.
3. The Wheatstone bridge and metre bridge are used to measure unknown resistances based on balancing a galvanometer using a sliding contact to adjust potential differences.
4. A potentiometer can be used to compare electromotive forces (EMFs) of cells by finding the balance point where the potential is equal and opposite to the cell's
Static electricity is an imbalance of electric charges within or on the surface of a material. It is created whenever two surfaces contact and separate, with at least one surface having a high resistance. The interaction of static electric charges is called electrostatics. Static electricity results from the triboelectric effect, where electrons are exchanged between materials on contact, resulting in one material becoming positively charged and the other negatively charged. Excess static charge can be removed or prevented by increasing moisture, using an air ionizer, or applying antistatic agents. Static discharge occurs as excess charge is neutralized by flowing to the surroundings, which can cause sparks responsible for industrial fires.
Electric potential difference (voltage)Jean Tralala
The document discusses concepts related to work, energy, and electric fields. It defines key terms like gravitational potential energy, gravitational potential, electric potential energy, electric potential, and electric potential difference. Gravitational potential energy and electric potential energy are defined as the energy stored in an object due to its position in a gravitational or electric field. Gravitational potential and electric potential refer to the potential energy per unit mass or charge. The electric potential difference between two points is the change in electric potential energy when a charge is moved between those points.
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.
This presentation is about electric potential. As we know, electric fields are vector quantities, which define electric field properties. The electric properties of space can also be described by electric potential. Electric potential is scaler. The concept of electric potential is more important due to its advantages over electric field as it has no direction which make it simpler. Electric potential is more practical than the electric field because differences in potential. Electric potentials and electric fields are associated with each other, and either can be used to describe the electrostatic properties of space. The gravitational potential energy is meaningful only in terms of the difference in potential energy in respect of reference point. The most important fact is that the Electric potential have similar characteristics as that of gravitational potential energy.
Photoelectric Effect And Dual Nature Of Matter And Radiation Class 12Self-employed
This document discusses the photoelectric effect and the dual wave-particle nature of matter and light. It covers:
1) An overview of the photoelectric effect and how it demonstrated the particle nature of light via Einstein's photoelectric equation.
2) De Broglie's hypothesis that matter has wave-like properties described by the de Broglie wavelength.
3) Daviesson and Germer's experiment demonstrating the wave-like diffraction of electrons from a crystal lattice, verifying matter waves.
The document provides information about current, electromotive force, potential difference, and resistance. It defines key terms, provides equations, and examples of calculations. It describes:
- Current is the flow of charge measured in amperes. It is carried by the flow of electrons in a conductor.
- Electromotive force is the work done per unit charge to drive charge around a complete circuit. It is measured in volts.
- Potential difference is the work done per unit charge to move charge through a circuit component. It is also measured in volts.
- Resistance is the opposition to current flow. It is calculated as potential difference divided by current and measured in ohms.
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
The document discusses various topics related to wave optics and the physics of light, including:
- The wave nature of light and how it explains phenomena like reflection, refraction, the formation of shadows and spectra.
- Huygens' principle which states that each point on a wavefront is the source of secondary wavelets and the new wavefront is the tangent to these wavelets.
- The laws of reflection which state that the angle of incidence equals the angle of reflection.
- Refraction and how the speed and wavelength of light changes when passing from one medium to another.
- Interference and coherence - the addition of waves to form a resultant wave, and how coherent sources are required
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.
The document discusses key concepts in electrostatics including the two types of electric charge - positive and negative. Objects can be charged through contact or rubbing and opposite charges are attracted while like charges repel. Charge is conserved in isolated systems and can be calculated using the equation Q=nqe, where n is the number of elementary charges and qe is the charge of an electron. The document also distinguishes between conductors and insulators based on how easily they allow charge to move through them.
class 12th physics (AC) alternating currents pptArpit Meena
1. The document discusses alternating current (AC) circuits and components. It covers topics like average and root mean square (RMS) values of AC current and voltage, AC circuits with resistors, inductors, capacitors, and their combinations.
2. It also discusses resonance in LCR circuits, power in AC circuits, wattless or idle current, and LC oscillations. Key points covered are impedance, phase relationships between current and voltage, factors affecting inductive and capacitive reactance, and definitions of quality factor.
3. Graphs show variations of inductive and capacitive reactance with frequency, the resonant curve, and damped versus undamped LC oscillations. Power formulas relate average power to RMS current
1. Electromagnetic induction occurs when a changing magnetic flux induces an electromotive force (emf) in a circuit. This was discovered by Faraday through his experiments.
2. Faraday's laws of induction state that an emf is induced in a circuit when the magnetic flux through the circuit changes, and that the magnitude of this induced emf is proportional to the rate of change of the magnetic flux.
3. Lenz's law describes the direction of the induced current: the current will flow in a direction that creates its own magnetic field to oppose the original change in magnetic flux that caused it. This ensures the conservation of energy.
This document provides an overview of basics in electrical engineering including electromagnetic induction, Lenz's law, Ampere's rule, and eddy currents. It was authored by Ms. Nishkam Dhiman, an assistant professor in the electrical engineering department at Chitkara Institute of Engineering & Technology. Key concepts covered include how electromagnetic induction causes current to flow when magnetic flux changes, how to determine the direction of induced current and force using hand rules, and how eddy currents are induced in conductors by changing magnetic fields.
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. 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.
1. Waves transfer energy from one place to another through a medium without transferring matter. They are produced by a vibrating or oscillating source and can be transverse or longitudinal.
2. Key wave properties include amplitude, wavelength, period, frequency, and speed. Amplitude is the maximum displacement from equilibrium, wavelength is the distance between peaks, period is time for one cycle, frequency is cycles per second, and speed depends on wavelength and frequency.
3. Waves can be characterized by displacement-time graphs showing oscillation over time or displacement-distance graphs showing the pattern of compression and rarefaction as the wave propagates through a medium.
Electricity is created by the interaction of positive protons and negative electrons. Electrons are attracted to protons, forming ions, and can move between atoms. Objects become electrically charged through friction, contact with another charged object, or induction, which is the redistribution of electrons. Electrical conductors like metals allow electron movement, while insulators do not. Electrical force follows Coulomb's law and is measured in volts. Electric current is the flow of electric charge through a conductor. Resistance opposes current and is measured in ohms according to Ohm's law. Electrical circuits use a voltage source to power devices by transferring energy.
Static electricity is a stationary electric charge built up on the surface of materials. It is caused by electrons being transferred between two objects during friction. There are two types of charges - positive and negative. Atoms contain protons which have a positive charge and electrons which have a negative charge. The laws of electrostatics state that like charges repel and unlike charges attract. Materials that allow charge to pass through are conductors, while insulators do not. When a charged object is brought near an uncharged object, the electric field can induce charges in the uncharged object. Some applications of static electricity include electrostatic precipitators, printers, and photocopiers. Grounding neutralizes charged objects by connecting them to the earth.
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.
In this relative motion and relative speed concept is demonstrated with help of examples, graphically and mathematically. The concepts of Einstein and Galileo
1. Electrostatics involves electric charges at rest, which arise from the particles that make up atoms. Atoms have equal numbers of protons and electrons, giving them a net neutral charge.
2. Objects can become charged through friction, induction, or conduction. Friction charging involves the transfer of electrons between two objects in contact. Induction charging uses a charged object to polarize a neutral object without direct contact.
3. The amount and type of charge on an object depends on whether it has an excess or deficit of electrons compared to protons. Coulomb's law describes the relationship between charged objects based on their relative charges and distance.
1. This document discusses several topics related to electricity including Kirchhoff's laws, Wheatstone bridge, metre bridge, and potentiometer.
2. Kirchhoff's laws include the junction rule which states the algebraic sum of currents at a junction is zero, and the loop rule which states the algebraic sum of potential drops around any closed loop is zero.
3. The Wheatstone bridge and metre bridge are used to measure unknown resistances based on balancing a galvanometer using a sliding contact to adjust potential differences.
4. A potentiometer can be used to compare electromotive forces (EMFs) of cells by finding the balance point where the potential is equal and opposite to the cell's
Static electricity is an imbalance of electric charges within or on the surface of a material. It is created whenever two surfaces contact and separate, with at least one surface having a high resistance. The interaction of static electric charges is called electrostatics. Static electricity results from the triboelectric effect, where electrons are exchanged between materials on contact, resulting in one material becoming positively charged and the other negatively charged. Excess static charge can be removed or prevented by increasing moisture, using an air ionizer, or applying antistatic agents. Static discharge occurs as excess charge is neutralized by flowing to the surroundings, which can cause sparks responsible for industrial fires.
Electric potential difference (voltage)Jean Tralala
The document discusses concepts related to work, energy, and electric fields. It defines key terms like gravitational potential energy, gravitational potential, electric potential energy, electric potential, and electric potential difference. Gravitational potential energy and electric potential energy are defined as the energy stored in an object due to its position in a gravitational or electric field. Gravitational potential and electric potential refer to the potential energy per unit mass or charge. The electric potential difference between two points is the change in electric potential energy when a charge is moved between those points.
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.
This presentation is about electric potential. As we know, electric fields are vector quantities, which define electric field properties. The electric properties of space can also be described by electric potential. Electric potential is scaler. The concept of electric potential is more important due to its advantages over electric field as it has no direction which make it simpler. Electric potential is more practical than the electric field because differences in potential. Electric potentials and electric fields are associated with each other, and either can be used to describe the electrostatic properties of space. The gravitational potential energy is meaningful only in terms of the difference in potential energy in respect of reference point. The most important fact is that the Electric potential have similar characteristics as that of gravitational potential energy.
Photoelectric Effect And Dual Nature Of Matter And Radiation Class 12Self-employed
This document discusses the photoelectric effect and the dual wave-particle nature of matter and light. It covers:
1) An overview of the photoelectric effect and how it demonstrated the particle nature of light via Einstein's photoelectric equation.
2) De Broglie's hypothesis that matter has wave-like properties described by the de Broglie wavelength.
3) Daviesson and Germer's experiment demonstrating the wave-like diffraction of electrons from a crystal lattice, verifying matter waves.
The document provides information about current, electromotive force, potential difference, and resistance. It defines key terms, provides equations, and examples of calculations. It describes:
- Current is the flow of charge measured in amperes. It is carried by the flow of electrons in a conductor.
- Electromotive force is the work done per unit charge to drive charge around a complete circuit. It is measured in volts.
- Potential difference is the work done per unit charge to move charge through a circuit component. It is also measured in volts.
- Resistance is the opposition to current flow. It is calculated as potential difference divided by current and measured in ohms.
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
The document discusses various topics related to wave optics and the physics of light, including:
- The wave nature of light and how it explains phenomena like reflection, refraction, the formation of shadows and spectra.
- Huygens' principle which states that each point on a wavefront is the source of secondary wavelets and the new wavefront is the tangent to these wavelets.
- The laws of reflection which state that the angle of incidence equals the angle of reflection.
- Refraction and how the speed and wavelength of light changes when passing from one medium to another.
- Interference and coherence - the addition of waves to form a resultant wave, and how coherent sources are required
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.
The document discusses key concepts in electrostatics including the two types of electric charge - positive and negative. Objects can be charged through contact or rubbing and opposite charges are attracted while like charges repel. Charge is conserved in isolated systems and can be calculated using the equation Q=nqe, where n is the number of elementary charges and qe is the charge of an electron. The document also distinguishes between conductors and insulators based on how easily they allow charge to move through them.
class 12th physics (AC) alternating currents pptArpit Meena
1. The document discusses alternating current (AC) circuits and components. It covers topics like average and root mean square (RMS) values of AC current and voltage, AC circuits with resistors, inductors, capacitors, and their combinations.
2. It also discusses resonance in LCR circuits, power in AC circuits, wattless or idle current, and LC oscillations. Key points covered are impedance, phase relationships between current and voltage, factors affecting inductive and capacitive reactance, and definitions of quality factor.
3. Graphs show variations of inductive and capacitive reactance with frequency, the resonant curve, and damped versus undamped LC oscillations. Power formulas relate average power to RMS current
1. Electromagnetic induction occurs when a changing magnetic flux induces an electromotive force (emf) in a circuit. This was discovered by Faraday through his experiments.
2. Faraday's laws of induction state that an emf is induced in a circuit when the magnetic flux through the circuit changes, and that the magnitude of this induced emf is proportional to the rate of change of the magnetic flux.
3. Lenz's law describes the direction of the induced current: the current will flow in a direction that creates its own magnetic field to oppose the original change in magnetic flux that caused it. This ensures the conservation of energy.
This document provides an overview of basics in electrical engineering including electromagnetic induction, Lenz's law, Ampere's rule, and eddy currents. It was authored by Ms. Nishkam Dhiman, an assistant professor in the electrical engineering department at Chitkara Institute of Engineering & Technology. Key concepts covered include how electromagnetic induction causes current to flow when magnetic flux changes, how to determine the direction of induced current and force using hand rules, and how eddy currents are induced in conductors by changing magnetic fields.
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. 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 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.
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.
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 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.
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.
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.
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.
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.
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 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 describes electric potential and how it relates to electric potential energy and electric field. It defines electric potential (V) as the electric potential energy per unit charge at a point. V is a scalar quantity. The potential difference between two points is equal to the work done by the electric field to move a test charge between the points. Equipotential surfaces connect all points of equal potential. The potential due to a point charge or group of point charges can be calculated using equations provided.
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.
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.
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.
The document discusses electric and magnetic fields. It defines electric field lines and how they point away from positive charges and toward negative charges. It provides the equation for calculating electric field strength from a point charge and the equation for calculating electric force from an electric field. It also discusses magnetic fields, including how current-carrying wires create magnetic fields and how charged particles experience a force in a magnetic field. Sample problems demonstrate using the right-hand rules to determine direction of magnetic forces.
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
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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.
Earth
Earth’s surface
10 kg
98 N
m
F
uniform field
nonuniform
field
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.
-
- - - - - - - - - - - - - -
q
F
q
F
uniform field
nonuniform
field
+
+
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:
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.
E = F/q.
5. Electric & Gravitational Fields Compared
Field
strength
Force
Intrinsic
Property
SI units
g = W / m N/kg
E = FE / q N/C
Gravity:
Electric
Force:
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 15s? (Hints on
next slide.)
E
-
7. Sample Problem Hints
qE
mg
E
-
1. Draw a vector as shown. Note that
FE = qE, by definition of E, and
that FE is to the left (opposite E)
since the charge is negative.
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
surrounding a field charge
Isolated, positive point
charge and its electric field
9. Single Positive Field Charge
+
This is a 2D picture
of the field lines that
surround a positive
field charge that is
either point-like or
spherically
symmetric. Not
shown are field lines
going out of and into
the page. Keep in
mind that the field
lines radiate
outwards because,
by definition, an
electric field vector
points in the
direction of the force
on a positive test
charge.
The nearer you
get to the
charge, the
more uniform
and stronger
the field.
Farther away
the field
strength gets
weaker, as
indicated by
the field lines
becoming
more spread
out.
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
+1
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.
+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.)
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.
A
B
C
D
14. Multiple Charges: How to Determine the Field
+ +Q1
Q2
To determine the field surrounding two field charges, Q1 and Q2, we pick
some points in the vicinity and place test charges there (red dots). Q1
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
this at many different points, we
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:
where K = 9 × 109
Nm2
/C2
(constant).
F =
KQq
r2
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
KQq / r2
E =
F
q
=
q
KQ
r2
=
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
GMm / r2
g =
F
m
=
m
GM
r2
=
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. + +
• 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.
Two + Field Charges of Different Magnitude
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. +
+
-
• 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
Positive Charge Near a Neutral Conductor
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
Earth’s surface
m
mg
Negatively charged surface
qE
+qg E
To lift an object of mass m a height h in a uniform gravitational field
g without acceleration, you must apply a force mg. The work you do
is +mgh, while the work done by the field is - mgh. 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 qE. You do positive work in lifting
the charge, and the field does negative work. The signs reverse when
you lower the charge.
28. Fields: Work & Potential Energy
Earth’s surface
m
mg
Negatively charged surface
qE
+qg E
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 = mg∆h for a mass in a gravitational field and ∆U = qE∆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.
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 - qEd - |Wfric|
= ∆K by the work-energy theorem.
q
FA
qE
d
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.
+
+
+
+
+
-
-
-
-
-
q
2. q is negative and displaced to the right.
4. q is negative and displaced to the left.
3. q is positive and displaced to the left.
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 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.
U / m = mgh / m = gh.
Earth’s surface
m
Negatively charged surface
q
g E
M
Q
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 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.
U / q = qEd / q = Ed.
h d
32. SI Units for Potential
By definition, electric potential is potential energy per unit charge. So,
V =
U
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:
1 V =
1 J
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. Earth’s surface Positively charged surface
Equipotential Surfaces
10 J/kg
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.
0 J/kg
20 J/kg
30 J/kg
40 J/kg
-15 V
0 V
-30 V
-45 V
-60 V
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.
side view
top view
not steep
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 +3C charge placed on the -70 V
surface has a potential energy of
-210 J.
-
37. Equipotentials Surfaces for Multiple-charge Configurations
+
-
Link
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
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
is the same as the straight-line path.
In either case each coulomb of
charge gains 10 J of potential energy.
No matter what path is taken:
∆VC→A = -20 V, and ∆VD→A = 0.
70V
80
V
90V
100V
A B
∆V is independent of path!
D
C
From A to D along the equipotential the
field can do no work, since the
displacement if always to E, which is
|| to F. Recall: W = F · x = F x cosθ.
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. Parallel Plate Capacitor
Area, A
+Q
-Q
d
battery
capacitor
V
The simplest type of capacitor is a
parallel plate capacitor, which consists
of two parallel metal plates, each of
area A, separated by a distance d. When
one plate is attached via a wire to the +
terminal of a battery, and the other plate
is connected to the - terminal, the
battery pulls e-’
s from the plate
connected to the - terminal and
deposits them on the other. As a whole
i
C
V
+Q -Q
wire
the capacitor remains neutral, but we say it now has a
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
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
same as that of the battery, V, the charging ceases. The
capacitor can remain charged even when disconnected from
the battery. Note the symbols used in the circuit diagram to
41. 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.
Parallel Plate Capacitor: E & U
- - - - - - - -
+ + + + + + + +
42. Capacitance
C
V
Q
Q = CV
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:
Ex: A 12 V battery will cause a capacitor to store
twice as much charge as a 6 V battery. Also, if
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.
C depends on the type of the capacitor. For a
parallel plate capacitor, C is proportional to the
area, A and inversely proportional to the plate
separation, d.
43. Capacitance: SI Units
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).
Q = CV
implies 1 C = (1 F)(1 V)
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:
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?
3.5 cm2
-1.62 μC
1.3 mm
20 V
+1.62 μC
From Q = CV, 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.
45. V = Ed
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
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 = mgh
electric: U = qEd ⇒ U/q = Ed ⇒ V = E d
46. V = Ed (formal derivation)
V =
U
q
(from the definition of potential)
V =
|Wfield|
q
(since W = F d )V=
F d
q
∆V= Ed (since E =
F
q
(since Wfield = - ∆U )
)
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
ExperimentA 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, mg, 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 = mg/ E = mgd / 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…
-
mg
qE
switch
d
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.
_
_
_
_
_
_
___
_
_
_
_
_
_
_
__ _ _ _
_
_
_
_
_
_
_ _ _
_
_
_
_
_
_
_
___ _
_
_
_
uniform R, uniform charge density
small R, high
charge density
large R, low
charge density
vector forces due to neighboring charges
53. Electric Fields In & Around Charged Conductors
_
_
_
_
_
_
___
_
_
_
_
_
_
_
__ _
_ _
_
_
_
_
_
_
_ _ _
_
_
_
_
_
_
_
___ _
_
_
_
small R,
strong E
E = 0
inside
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.
E = 0
inside
E is radially symmetric outside.
large R,
weak E
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