The document summarizes key concepts about magnetism and magnetic fields from the physics textbook "Physics II" by Robert Resnick and David Halliday.
In 3 sentences:
The document discusses the historical discoveries of magnetism dating back to ancient Greece. It then explains the fundamental properties of magnetic fields including magnetic poles, the magnetic force on moving charges, and the relationship between electric currents and magnetic fields as described by the Biot-Savart law and Ampere's law. Several examples are also provided to illustrate applications of these fundamental magnetic field equations.
The document summarizes key concepts about magnetism and magnetic fields from the physics textbook "Physics II" by Robert Resnick and David Halliday.
In 3 sentences:
The document discusses the historical discoveries of magnetism dating back to ancient Greece and China. It then explains the fundamental properties of magnetic fields such as magnetic poles, the magnetic force on moving charges, and the relationship between electric currents and magnetic fields as described by the Biot-Savart law and Ampere's law. Several examples are also provided to illustrate how to calculate magnetic fields generated by straight wires and solenoids.
1) The Biot-Savart law describes the magnetic field generated by a current-carrying conductor. It states that the magnetic field is proportional to the current and inversely proportional to the distance from the current element.
2) The direction of the magnetic field generated by a current element is perpendicular to both the current element and the line from the current element to the point where the magnetic field is calculated.
3) Examples of applying the Biot-Savart law include calculating the magnetic field generated by a circular loop of wire and along the axis of a solenoid. The magnetic fields add linearly for multiple current elements.
24 pius augustine em induction & acPiusAugustine
1. The document discusses the principles of electromagnetic induction, including Faraday's law and Lenz's law. It provides explanations and examples of motional EMF, factors affecting induced EMF, and applications of electromagnetic induction such as generators and eddy currents.
2. Key experiments are described, such as Michael Faraday's coil-magnet experiment which demonstrated that a changing magnetic field can induce an electric current in a loop of wire.
3. Applications of electromagnetic induction discussed include generators, transformers, eddy current brakes, induction furnaces, and traffic light triggers.
Hans Christian Oersted discovered in 1819 that a compass needle is deflected by a current-carrying wire, demonstrating the relationship between electricity and magnetism. A current produces a circular magnetic field around it, and the direction of the magnetic field can be determined using the Right-Hand Grip rule. Maxwell's equations relate electric and magnetic fields and show that changing magnetic fields produce electric fields and vice versa. Magnetic fields exert forces on moving charges and electric currents. These forces allow applications like electromagnets, electric motors, and particle accelerators.
This document discusses various topics related to magnetism including:
1. The properties of bar magnets such as having two poles and aligning along the north-south axis.
2. Current loops and solenoids can also act as magnets with a magnetic dipole moment.
3. The magnetic field due to a dipole follows an inverse cube law and the torque on a dipole in a uniform field is proportional to the magnetic moment.
4. Earth has its own magnetic field with a magnetic axis inclined to the geographic axis, and this field exhibits properties like declination and dip.
5. Materials are classified as diamagnetic, paramagnetic or ferromagnetic based on their relative permeability and
This document provides an introduction to magnetostatics. It defines key concepts such as magnetic fields, magnetic flux, magnetic flux density, current, current density, and more. It discusses Oersted's experiment which showed the connection between electricity and magnetism. Rules for determining the direction of magnetic fields, such as Maxwell's corkscrew rule and the right hand grip rule, are presented. Biot-Savart's law, which gives the magnetic field produced by a current-carrying element, is also covered.
1. A proton moves through Earth's magnetic field with a speed of 1.00 x 105 m/s.
2. The magnetic field at this location has a value of 55.0μT.
3. We need to determine the magnetic force on the proton when it moves perpendicular to the magnetic field lines.
Using the formula for magnetic force, F=qvB, where q is the charge on the proton (1.60x10-19 C), v is its speed, and B is the magnetic field:
F= (1.60x10-19 C) x (1.00 x
Electromagnetism is the production of a magnetic field by an electric current. Oersted discovered the magnetic effect of current in 1820 through an experiment showing a magnetic needle deflecting when a current was passed through a nearby wire. The magnetic field strength increases with increasing current and vice versa. According to Biot-Savart law, the magnetic field produced by a current-carrying conductor depends on the current, distance from the conductor, and angle between the conductor and field point.
The document summarizes key concepts about magnetism and magnetic fields from the physics textbook "Physics II" by Robert Resnick and David Halliday.
In 3 sentences:
The document discusses the historical discoveries of magnetism dating back to ancient Greece and China. It then explains the fundamental properties of magnetic fields such as magnetic poles, the magnetic force on moving charges, and the relationship between electric currents and magnetic fields as described by the Biot-Savart law and Ampere's law. Several examples are also provided to illustrate how to calculate magnetic fields generated by straight wires and solenoids.
1) The Biot-Savart law describes the magnetic field generated by a current-carrying conductor. It states that the magnetic field is proportional to the current and inversely proportional to the distance from the current element.
2) The direction of the magnetic field generated by a current element is perpendicular to both the current element and the line from the current element to the point where the magnetic field is calculated.
3) Examples of applying the Biot-Savart law include calculating the magnetic field generated by a circular loop of wire and along the axis of a solenoid. The magnetic fields add linearly for multiple current elements.
24 pius augustine em induction & acPiusAugustine
1. The document discusses the principles of electromagnetic induction, including Faraday's law and Lenz's law. It provides explanations and examples of motional EMF, factors affecting induced EMF, and applications of electromagnetic induction such as generators and eddy currents.
2. Key experiments are described, such as Michael Faraday's coil-magnet experiment which demonstrated that a changing magnetic field can induce an electric current in a loop of wire.
3. Applications of electromagnetic induction discussed include generators, transformers, eddy current brakes, induction furnaces, and traffic light triggers.
Hans Christian Oersted discovered in 1819 that a compass needle is deflected by a current-carrying wire, demonstrating the relationship between electricity and magnetism. A current produces a circular magnetic field around it, and the direction of the magnetic field can be determined using the Right-Hand Grip rule. Maxwell's equations relate electric and magnetic fields and show that changing magnetic fields produce electric fields and vice versa. Magnetic fields exert forces on moving charges and electric currents. These forces allow applications like electromagnets, electric motors, and particle accelerators.
This document discusses various topics related to magnetism including:
1. The properties of bar magnets such as having two poles and aligning along the north-south axis.
2. Current loops and solenoids can also act as magnets with a magnetic dipole moment.
3. The magnetic field due to a dipole follows an inverse cube law and the torque on a dipole in a uniform field is proportional to the magnetic moment.
4. Earth has its own magnetic field with a magnetic axis inclined to the geographic axis, and this field exhibits properties like declination and dip.
5. Materials are classified as diamagnetic, paramagnetic or ferromagnetic based on their relative permeability and
This document provides an introduction to magnetostatics. It defines key concepts such as magnetic fields, magnetic flux, magnetic flux density, current, current density, and more. It discusses Oersted's experiment which showed the connection between electricity and magnetism. Rules for determining the direction of magnetic fields, such as Maxwell's corkscrew rule and the right hand grip rule, are presented. Biot-Savart's law, which gives the magnetic field produced by a current-carrying element, is also covered.
1. A proton moves through Earth's magnetic field with a speed of 1.00 x 105 m/s.
2. The magnetic field at this location has a value of 55.0μT.
3. We need to determine the magnetic force on the proton when it moves perpendicular to the magnetic field lines.
Using the formula for magnetic force, F=qvB, where q is the charge on the proton (1.60x10-19 C), v is its speed, and B is the magnetic field:
F= (1.60x10-19 C) x (1.00 x
Electromagnetism is the production of a magnetic field by an electric current. Oersted discovered the magnetic effect of current in 1820 through an experiment showing a magnetic needle deflecting when a current was passed through a nearby wire. The magnetic field strength increases with increasing current and vice versa. According to Biot-Savart law, the magnetic field produced by a current-carrying conductor depends on the current, distance from the conductor, and angle between the conductor and field point.
Unit 3 Magnetism and effect of currentMahesh Kumar
Unit 3 Magnetis and Effect of current.
Notes with derivation as well as important question are also marked for your convenience
Images are also attached..
Magnetism has been observed for over 2000 years, with lodestones found in ancient Greece exhibiting magnetic properties. In the 1820s, Hans Christian Oersted discovered the relationship between electricity and magnetism when an electric current caused a compass needle to deflect. Magnets have both north and south poles and magnetic fields that exert forces on other magnetic and electrically charged objects. The strength of this magnetic force depends on factors like the distance from the magnet, the velocity and charge of the object, and the magnetic field strength.
This document discusses the Biot-Savart law and its use in calculating magnetic fields. It begins by describing Biot and Savart's experimental observations which led to the mathematical expression of the Biot-Savart law. It then provides examples of using the law to calculate the magnetic field of a circular current loop and an ideal solenoid. For the solenoid, Ampere's law is used to derive an expression showing the interior magnetic field is directly proportional to the current and number of turns per unit length.
1) The document discusses magnetic fields, field lines, and the forces experienced by moving charges in magnetic fields.
2) It explains that a magnetic field extends through all space and is represented by magnetic field lines. A magnetic dipole field leaves the North pole and enters the South pole.
3) The magnetic force on a moving charge is perpendicular to both the magnetic field and the velocity of the charge, and is given by the equation F=qv×B.
This document provides an overview of key concepts in waves and sound from Chapter 16. It covers the nature of waves including transverse and longitudinal waves. It discusses topics like speed of waves on a string, mathematical description of waves, nature of sound, and speed of sound. The document is structured with learning objectives, tables of contents, definitions of terms, examples, and conceptual questions.
1. The document describes an experiment to measure and plot the B-H curve and permeability curve of a given material using a data logger, power supply, coils, cores and sensors.
2. A transformer is used to generate a magnetic field by passing a current through the primary coil, and the induced voltage in the secondary coil is measured to calculate the magnetic flux density B.
3. For a ferromagnetic material, B varies non-linearly with the magnetic field H, forming a hysteresis loop on the B-H curve whose area indicates energy loss per cycle.
1) Magnets have north and south poles that attract or repel each other depending on their orientation, similar to electric charges. The magnetic force follows a law analogous to Newton's law of gravity and Coulomb's law for electricity.
2) If a magnet is broken in half, each new piece becomes a smaller magnet with its own north and south poles, rather than separating the original poles.
3) Passing an electric current through a coil of wire or loop creates a magnetic field. The direction and strength of the magnetic field can be determined using the right hand rule.
General Relativity and gravitational waves: a primerJoseph Fernandez
A short introduction to the one of the nicest bits of physical reasoning ever, which led to Albert Einstein's General Relativity, gravitational waves and our research on gravitational wave sources.
Designed by Joseph John Fernandez for LJMU FET Research Week.
After reading this module, you should be able to . . .
10.01 Identify that if all parts of a body rotate around a fixed
axis locked together, the body is a rigid body. (This chapter
is about the motion of such bodies.)
10.02 Identify that the angular position of a rotating rigid body
is the angle that an internal reference line makes with a
fixed, external reference line.
10.03 Apply the relationship between angular displacement
and the initial and final angular positions.
10.04 Apply the relationship between average angular velocity, angular displacement, and the time interval for that displacement.
10.05 Apply the relationship between average angular acceleration, change in angular velocity, and the time interval for
that change.
10.06 Identify that counterclockwise motion is in the positive
direction and clockwise motion is in the negative direction.
10.07 Given angular position as a function of time, calculate the
instantaneous angular velocity at any particular time and the
average angular velocity between any two particular times.
10.08 Given a graph of angular position versus time, determine the instantaneous angular velocity at a particular time
and the average angular velocity between any two particular times.
10.09 Identify instantaneous angular speed as the magnitude
of the instantaneous angular velocity.
10.10 Given angular velocity as a function of time, calculate
the instantaneous angular acceleration at any particular
time and the average angular acceleration between any
two particular times.
10.11 Given a graph of angular velocity versus time, determine the instantaneous angular acceleration at any particular time and the average angular acceleration between
any two particular times.
10.12 Calculate a body’s change in angular velocity by
integrating its angular acceleration function with respect
to time.
10.13 Calculate a body’s change in angular position by integrating its angular velocity function with respect to time.
7-1 KINETIC ENERGY
After reading this module, you should be able to . . .
7.01 Apply the relationship between a particle’s kinetic
energy, mass, and speed.
7.02 Identify that kinetic energy is a scalar quantity.
7-2 WORK AND KINETIC ENERGY
After reading this module, you should be able to . . .
7.03 Apply the relationship between a force (magnitude and
direction) and the work done on a particle by the force
when the particle undergoes a displacement.
7.04 Calculate work by taking a dot product of the force vector and the displacement vector, in either magnitude-angle
or unit-vector notation.
7.05 If multiple forces act on a particle, calculate the net work
done by them.
7.06 Apply the work–kinetic energy theorem to relate the
work done by a force (or the net work done by multiple
forces) and the resulting change in kinetic energy. etc...
The document contains a multi-part conceptual physics problem about magnetic induction.
Part 1 asks about orienting a sheet of paper at the magnetic equator to maximize or minimize magnetic flux through it. Part 2 shows that the units T⋅m2/s are equivalent to volts. Part 3 asks about the direction of induced current in a conducting loop based on the direction and changing magnitude of an applied magnetic field.
The document discusses magnetostatics and provides definitions and explanations of key concepts including magnetic field, magnetic flux, Biot-Savart law, Ampere's law, solenoids, ballistic galvanometers, and damping conditions. Specific topics covered include the magnetic field produced by steady currents, magnetic field lines, curl and divergence of magnetic fields, theory and operation of ballistic galvanometers, and current and charge sensitivity of galvanometers. Examples and derivations of equations for magnetic fields and forces on conductors in fields are also provided.
Fundamentasl of Physics "CENTER OF MASS AND LINEAR MOMENTUM"Muhammad Faizan Musa
(1) The document discusses determining the center of mass (com) of systems of particles and extended objects.
(2) The com of a system of particles is defined as the point where the total mass of the system could be concentrated and behave as if forces were applied at that point.
(3) For a system of n particles, the com is calculated using the positions and masses of the individual particles.
(4) For continuous distributions of mass like solid objects, the com is determined using integrals over the object's mass distribution.
This document summarizes key concepts from a chapter on magnetic fields. It discusses the magnetic field created by a current-carrying wire, which is perpendicular to the wire. It also describes how a current loop acts as a magnet, with a magnetic dipole moment proportional to the current and area of the loop. Additionally, it covers Ampere's law relating the line integral of magnetic field around a closed loop to the current passing through the enclosed area.
1. Electric currents flowing in wires produce magnetic fields around the wires. The direction of the magnetic field can be determined using the right-hand grip rule.
2. A wire carrying a current experiences a force when placed in a magnetic field. The direction of this force can be determined using Fleming's left-hand rule. Charged particles also experience a force in a magnetic field.
3. Parallel wires with currents in the same direction attract, while parallel wires with currents in opposite directions repel. This is due to the interaction of the magnetic fields produced by each current.
2.BH curve hysteresis in ferro ferrimagnetsNarayan Behera
The document discusses different types of magnetism including diamagnetism, paramagnetism, and ferromagnetism. It describes the B-H hysteresis curve method for measuring hysteresis loops using an AC inductance technique. The hysteresis loop provides information about magnetic properties like coercivity, remanence, and hysteresis losses. Domain theory is introduced to explain hysteresis in terms of irreversible domain wall motion within a ferromagnetic material.
[Electricity and Magnetism] ElectrodynamicsManmohan Dash
We discussed extensively the electromagnetism course for an engineering 1st year class. This is also useful for ‘hons’ and ‘pass’ Physics students.
This was a course I delivered to engineering first years, around 9th November 2009. I added all the diagrams and many explanations only now; 21-23 Aug 2015.
Next; Lectures on ‘electromagnetic waves’ and ‘Oscillations and Waves’. You can write me at g6pontiac@gmail.com or visit my website at http://mdashf.org
1) Magnets have north and south poles that attract or repel each other depending on their orientation. They generate magnetic fields around them represented by field lines.
2) Charged particles experience a magnetic force when moving through a magnetic field that is perpendicular to both the field and velocity directions. The right hand rule determines the force direction.
3) Current-carrying wires also experience a magnetic force when placed in an external magnetic field due to their internal magnetic field generated by the current.
1. The document discusses various topics related to waves, optics, oscillation, and gravitation. It defines key terms like traveling waves, standing waves, and wave propagation.
2. Important concepts are covered, including the principle of superposition, simple harmonic motion, Newton's laws of gravitation, and Kepler's laws of planetary motion.
3. Examples are provided to demonstrate applications of these concepts, such as calculating spring oscillation properties and determining values related to a vibrating string and pendulum motion.
1) The document discusses self-induction and back emf in circuits containing coils or inductors. When the current through a coil changes, it produces a back emf opposing the change due to Lenz's law.
2) It also describes how transformers work using mutual induction between two coils. The primary coil is connected to a changing current that induces a current in the secondary coil.
3) Transformers can be used to change voltages by adjusting the turn ratios of the coils. They allow efficient long-distance power transmission by stepping voltages up for transmission and down for usage.
This document contains examples of calculating electromagnetic induction in coils and coupled inductors. It provides the formulas and steps to calculate:
1) The emf induced in a moving conductor in a magnetic field for different orientations.
2) The average emf induced in a coil when the current reversing over time causes the magnetic flux to change.
3) The mutual inductance and induced emf in two coupled coils when the current in one coil changes.
4) The self and mutual inductances, coupling coefficient, and equivalent inductance of coupled coils.
1) The document discusses coupled coils and how to calculate their equivalent inductance whether in series aiding, series opposing, or parallel configurations.
2) It provides the equations to calculate the equivalent inductance based on the individual coil inductances and mutual inductance.
3) An example problem is shown of calculating the individual coil inductances and mutual inductance given the equivalent inductance of two coils connected in series aiding.
Unit 3 Magnetism and effect of currentMahesh Kumar
Unit 3 Magnetis and Effect of current.
Notes with derivation as well as important question are also marked for your convenience
Images are also attached..
Magnetism has been observed for over 2000 years, with lodestones found in ancient Greece exhibiting magnetic properties. In the 1820s, Hans Christian Oersted discovered the relationship between electricity and magnetism when an electric current caused a compass needle to deflect. Magnets have both north and south poles and magnetic fields that exert forces on other magnetic and electrically charged objects. The strength of this magnetic force depends on factors like the distance from the magnet, the velocity and charge of the object, and the magnetic field strength.
This document discusses the Biot-Savart law and its use in calculating magnetic fields. It begins by describing Biot and Savart's experimental observations which led to the mathematical expression of the Biot-Savart law. It then provides examples of using the law to calculate the magnetic field of a circular current loop and an ideal solenoid. For the solenoid, Ampere's law is used to derive an expression showing the interior magnetic field is directly proportional to the current and number of turns per unit length.
1) The document discusses magnetic fields, field lines, and the forces experienced by moving charges in magnetic fields.
2) It explains that a magnetic field extends through all space and is represented by magnetic field lines. A magnetic dipole field leaves the North pole and enters the South pole.
3) The magnetic force on a moving charge is perpendicular to both the magnetic field and the velocity of the charge, and is given by the equation F=qv×B.
This document provides an overview of key concepts in waves and sound from Chapter 16. It covers the nature of waves including transverse and longitudinal waves. It discusses topics like speed of waves on a string, mathematical description of waves, nature of sound, and speed of sound. The document is structured with learning objectives, tables of contents, definitions of terms, examples, and conceptual questions.
1. The document describes an experiment to measure and plot the B-H curve and permeability curve of a given material using a data logger, power supply, coils, cores and sensors.
2. A transformer is used to generate a magnetic field by passing a current through the primary coil, and the induced voltage in the secondary coil is measured to calculate the magnetic flux density B.
3. For a ferromagnetic material, B varies non-linearly with the magnetic field H, forming a hysteresis loop on the B-H curve whose area indicates energy loss per cycle.
1) Magnets have north and south poles that attract or repel each other depending on their orientation, similar to electric charges. The magnetic force follows a law analogous to Newton's law of gravity and Coulomb's law for electricity.
2) If a magnet is broken in half, each new piece becomes a smaller magnet with its own north and south poles, rather than separating the original poles.
3) Passing an electric current through a coil of wire or loop creates a magnetic field. The direction and strength of the magnetic field can be determined using the right hand rule.
General Relativity and gravitational waves: a primerJoseph Fernandez
A short introduction to the one of the nicest bits of physical reasoning ever, which led to Albert Einstein's General Relativity, gravitational waves and our research on gravitational wave sources.
Designed by Joseph John Fernandez for LJMU FET Research Week.
After reading this module, you should be able to . . .
10.01 Identify that if all parts of a body rotate around a fixed
axis locked together, the body is a rigid body. (This chapter
is about the motion of such bodies.)
10.02 Identify that the angular position of a rotating rigid body
is the angle that an internal reference line makes with a
fixed, external reference line.
10.03 Apply the relationship between angular displacement
and the initial and final angular positions.
10.04 Apply the relationship between average angular velocity, angular displacement, and the time interval for that displacement.
10.05 Apply the relationship between average angular acceleration, change in angular velocity, and the time interval for
that change.
10.06 Identify that counterclockwise motion is in the positive
direction and clockwise motion is in the negative direction.
10.07 Given angular position as a function of time, calculate the
instantaneous angular velocity at any particular time and the
average angular velocity between any two particular times.
10.08 Given a graph of angular position versus time, determine the instantaneous angular velocity at a particular time
and the average angular velocity between any two particular times.
10.09 Identify instantaneous angular speed as the magnitude
of the instantaneous angular velocity.
10.10 Given angular velocity as a function of time, calculate
the instantaneous angular acceleration at any particular
time and the average angular acceleration between any
two particular times.
10.11 Given a graph of angular velocity versus time, determine the instantaneous angular acceleration at any particular time and the average angular acceleration between
any two particular times.
10.12 Calculate a body’s change in angular velocity by
integrating its angular acceleration function with respect
to time.
10.13 Calculate a body’s change in angular position by integrating its angular velocity function with respect to time.
7-1 KINETIC ENERGY
After reading this module, you should be able to . . .
7.01 Apply the relationship between a particle’s kinetic
energy, mass, and speed.
7.02 Identify that kinetic energy is a scalar quantity.
7-2 WORK AND KINETIC ENERGY
After reading this module, you should be able to . . .
7.03 Apply the relationship between a force (magnitude and
direction) and the work done on a particle by the force
when the particle undergoes a displacement.
7.04 Calculate work by taking a dot product of the force vector and the displacement vector, in either magnitude-angle
or unit-vector notation.
7.05 If multiple forces act on a particle, calculate the net work
done by them.
7.06 Apply the work–kinetic energy theorem to relate the
work done by a force (or the net work done by multiple
forces) and the resulting change in kinetic energy. etc...
The document contains a multi-part conceptual physics problem about magnetic induction.
Part 1 asks about orienting a sheet of paper at the magnetic equator to maximize or minimize magnetic flux through it. Part 2 shows that the units T⋅m2/s are equivalent to volts. Part 3 asks about the direction of induced current in a conducting loop based on the direction and changing magnitude of an applied magnetic field.
The document discusses magnetostatics and provides definitions and explanations of key concepts including magnetic field, magnetic flux, Biot-Savart law, Ampere's law, solenoids, ballistic galvanometers, and damping conditions. Specific topics covered include the magnetic field produced by steady currents, magnetic field lines, curl and divergence of magnetic fields, theory and operation of ballistic galvanometers, and current and charge sensitivity of galvanometers. Examples and derivations of equations for magnetic fields and forces on conductors in fields are also provided.
Fundamentasl of Physics "CENTER OF MASS AND LINEAR MOMENTUM"Muhammad Faizan Musa
(1) The document discusses determining the center of mass (com) of systems of particles and extended objects.
(2) The com of a system of particles is defined as the point where the total mass of the system could be concentrated and behave as if forces were applied at that point.
(3) For a system of n particles, the com is calculated using the positions and masses of the individual particles.
(4) For continuous distributions of mass like solid objects, the com is determined using integrals over the object's mass distribution.
This document summarizes key concepts from a chapter on magnetic fields. It discusses the magnetic field created by a current-carrying wire, which is perpendicular to the wire. It also describes how a current loop acts as a magnet, with a magnetic dipole moment proportional to the current and area of the loop. Additionally, it covers Ampere's law relating the line integral of magnetic field around a closed loop to the current passing through the enclosed area.
1. Electric currents flowing in wires produce magnetic fields around the wires. The direction of the magnetic field can be determined using the right-hand grip rule.
2. A wire carrying a current experiences a force when placed in a magnetic field. The direction of this force can be determined using Fleming's left-hand rule. Charged particles also experience a force in a magnetic field.
3. Parallel wires with currents in the same direction attract, while parallel wires with currents in opposite directions repel. This is due to the interaction of the magnetic fields produced by each current.
2.BH curve hysteresis in ferro ferrimagnetsNarayan Behera
The document discusses different types of magnetism including diamagnetism, paramagnetism, and ferromagnetism. It describes the B-H hysteresis curve method for measuring hysteresis loops using an AC inductance technique. The hysteresis loop provides information about magnetic properties like coercivity, remanence, and hysteresis losses. Domain theory is introduced to explain hysteresis in terms of irreversible domain wall motion within a ferromagnetic material.
[Electricity and Magnetism] ElectrodynamicsManmohan Dash
We discussed extensively the electromagnetism course for an engineering 1st year class. This is also useful for ‘hons’ and ‘pass’ Physics students.
This was a course I delivered to engineering first years, around 9th November 2009. I added all the diagrams and many explanations only now; 21-23 Aug 2015.
Next; Lectures on ‘electromagnetic waves’ and ‘Oscillations and Waves’. You can write me at g6pontiac@gmail.com or visit my website at http://mdashf.org
1) Magnets have north and south poles that attract or repel each other depending on their orientation. They generate magnetic fields around them represented by field lines.
2) Charged particles experience a magnetic force when moving through a magnetic field that is perpendicular to both the field and velocity directions. The right hand rule determines the force direction.
3) Current-carrying wires also experience a magnetic force when placed in an external magnetic field due to their internal magnetic field generated by the current.
1. The document discusses various topics related to waves, optics, oscillation, and gravitation. It defines key terms like traveling waves, standing waves, and wave propagation.
2. Important concepts are covered, including the principle of superposition, simple harmonic motion, Newton's laws of gravitation, and Kepler's laws of planetary motion.
3. Examples are provided to demonstrate applications of these concepts, such as calculating spring oscillation properties and determining values related to a vibrating string and pendulum motion.
1) The document discusses self-induction and back emf in circuits containing coils or inductors. When the current through a coil changes, it produces a back emf opposing the change due to Lenz's law.
2) It also describes how transformers work using mutual induction between two coils. The primary coil is connected to a changing current that induces a current in the secondary coil.
3) Transformers can be used to change voltages by adjusting the turn ratios of the coils. They allow efficient long-distance power transmission by stepping voltages up for transmission and down for usage.
This document contains examples of calculating electromagnetic induction in coils and coupled inductors. It provides the formulas and steps to calculate:
1) The emf induced in a moving conductor in a magnetic field for different orientations.
2) The average emf induced in a coil when the current reversing over time causes the magnetic flux to change.
3) The mutual inductance and induced emf in two coupled coils when the current in one coil changes.
4) The self and mutual inductances, coupling coefficient, and equivalent inductance of coupled coils.
1) The document discusses coupled coils and how to calculate their equivalent inductance whether in series aiding, series opposing, or parallel configurations.
2) It provides the equations to calculate the equivalent inductance based on the individual coil inductances and mutual inductance.
3) An example problem is shown of calculating the individual coil inductances and mutual inductance given the equivalent inductance of two coils connected in series aiding.
This document discusses magnetic circuits and electromagnetic induction. It defines key terms like magnetic flux, magnetomotive force, reluctance, self-inductance, and mutual inductance. Faraday's laws of induction state that an electromotive force (EMF) is induced in a coil when the magnetic flux through the coil changes. Lenz's law specifies that the induced EMF will oppose the change that created it. Magnetic circuits can be modeled similarly to electric circuits, with magnetomotive force, magnetic flux, and reluctance analogous to voltage, current, and resistance.
The document discusses self-induced emf, self-inductance, mutually induced emf, and mutual inductance. It states that self-induced emf is proportional to the rate of change of current through a coil and self-inductance is the proportionality constant. Mutually induced emf occurs when the magnetic flux passing through one coil changes due to a changing current in another nearby coil, and mutual inductance is the proportionality constant between the induced emf and rate of change of current. The coupling coefficient k describes the degree of coupling between two coils and is defined as the ratio of mutual flux to self flux.
self inductance , mutual inductance and coeffecient of couplingsaahil kshatriya
This document discusses self-inductance and mutual inductance. It defines self-inductance as the phenomenon where an induced electromotive force (emf) is created within a coil due to a change in the current passing through the coil. It also defines mutual inductance as the induced emf created in one coil due to a change in current in a neighboring coil. The document provides equations for calculating the mutual inductance between two coils based on their geometry and number of turns. It states that the mutual inductance depends on the number of turns in each coil, their cross-sectional area, and distance between them.
This document discusses electromagnetic induction, including the motor and generator effects. It provides explanations and examples of how current flowing in a wire creates a magnetic field (motor effect), and how a changing magnetic field induces current in a conductor (generator effect). Right-hand rules are introduced to predict the direction of forces and currents. Examples are given for determining the direction of force on current-carrying wires and moving charges in magnetic fields.
NCERT Solutions for Moving Charges and Magnetism Class 12
Class 12 Physics typically covers the topic of moving charges and magnetism, which is an essential part of electromagnetism.
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This document provides an overview of magnetostatics and key concepts related to magnetism. It begins with a top ten list of magnetism principles. It then discusses the properties of magnetic poles, fields, and materials. Key points made include that every magnet has both a north and south pole, magnetic fields are generated by moving charges, and materials can be classified based on their magnetic permeability. The document also introduces critical magnetism concepts such as the Biot-Savart law, Ampere's law, magnetic dipoles, and the forces and energy associated with magnetic fields.
1. Hans Christian Oersted discovered that electric currents produce magnetic fields. He observed that a current-carrying wire deflected a nearby compass needle. This showed that moving electric charges create magnetic fields.
2. The direction of the magnetic field produced by a current can be determined using the right-hand rule. The force on a moving charge in a magnetic field depends on the charge, velocity, field strength, and their relative directions, as described by the Lorentz force law.
3. Magnetic fields can cause moving charges to travel in circular paths. The radius of the path is determined by the charge, velocity, and magnetic field strength. This explains phenomena like the bending of electron beams in cathode ray tubes
1. The document discusses Faraday's law of induction and induced electric fields. It summarizes that changing magnetic flux induces an electromotive force (emf) in a conductor.
2. Faraday's law states that the magnitude of induced emf is equal to the rate of change of magnetic flux through a conductor. A changing magnetic field also induces an electric field in space.
3. The document provides equations for calculating induced emf and electric fields. It also discusses Lenz's law, which describes the direction of induced current to oppose the change in magnetic flux that causes it.
The electric force between two charged particles is:
- Inversely proportional to the square of the distance between them
- Directed along the line joining the particles
- Attractive if charges have opposite signs, repulsive if the same
The electric field E at a point is defined as the electric force on a positive test charge at that point divided by the magnitude of the test charge. Electric field lines are drawn tangent to the field, with a higher density of lines indicating a greater field magnitude.
This document discusses electricity and magnetism. It provides information on the fundamental properties of magnets and magnetic fields. Some key points include:
- Magnetism and electricity are two aspects of a single phenomenon related to the motion of electric charges.
- Magnetic fields can be produced by electric currents in wires, as discovered by Oersted in 1820.
- Magnetic induction B is defined based on the force experienced by a moving charge in a magnetic field.
- Materials can be classified as ferromagnetic, paramagnetic, or diamagnetic based on their behavior in magnetic fields. Permeability and susceptibility quantify a material's response to magnetic fields.
- Faraday's experiment demonstrated that a changing magnetic field can induce an electric current in a nearby conductor. He showed this by inducing currents in a secondary coil wrapped around a ring using the changing magnetic field from a primary coil with a switch-controlled current.
- Faraday's law of induction states that the induced emf in a circuit is directly proportional to the rate of change of the magnetic flux through the circuit. A changing magnetic field induces currents that oppose the change according to Lenz's law.
- Examples are given demonstrating how Lenz's law predicts the direction of induced currents based on producing a magnetic field that opposes the change causing it.
This document discusses various topics related to magnetism including:
1. The properties of bar magnets such as poles attracting and repelling and aligning along the North-South axis.
2. Magnetic fields created by current loops and solenoids which behave similarly to bar magnets.
3. Key terms like magnetic dipole moment, magnetic permeability, and hysteresis.
4. Earth's magnetic field including declination, dip, horizontal and vertical components.
5. The differences between diamagnetic, paramagnetic and ferromagnetic materials and their behavior in magnetic fields.
6. Curie's law relating magnetic susceptibility to temperature.
1. A magnetic field B is defined in terms of the force FB acting on a charged particle q moving with velocity v through the field.
2. A charged particle moving perpendicular to a uniform B will travel in a circle, with radius r given by qB/mv. The frequency f, angular frequency ω, and period T of circular motion are also defined.
3. A current-carrying wire in a uniform B experiences a sideways force F=BIL, where I is the current and L a vector in the current direction. The force on a current element idL is idLB.
4. A coil in a uniform B feels a torque τ=μxB, where μ is the coil
1. A magnetic field B is defined in terms of the force FB acting on a charged particle q moving with velocity v through the field.
2. A charged particle moving perpendicular to a uniform B will travel in a circle, with radius r given by qB/mv. The frequency f, angular frequency ω, and period T of circular motion are also defined.
3. A current-carrying wire in a uniform B experiences a sideways force F=BIL, where I is the current and L a length vector in the current direction. The force on a current element idL is given by idLB.
4. A coil in a uniform B experiences a torque τ=μ×B, where
This document discusses various topics related to magnetism including:
1. The properties of bar magnets such as aligning along north-south, opposite poles attracting and like poles repelling, and inducing magnetism in other materials.
2. Current loops and solenoids behaving as magnetic dipoles with a magnetic dipole moment proportional to the current and area.
3. Coulomb's law applied to magnetism with the force between poles inversely proportional to the square of the distance between them.
4. Key terms such as magnetic field strength, magnetic flux, permeability, susceptibility, and magnetization.
5. The magnetic field created by a magnetic dipole falling off with the cube
This document discusses various topics related to magnetism including:
1. The properties of bar magnets such as poles attracting and repelling and aligning along the North-South axis.
2. Current loops and solenoids behaving as magnetic dipoles with a magnetic dipole moment.
3. Coulomb's law applied to magnetism describing the force between magnetic poles.
4. Key terms such as magnetic field strength, magnetic flux, permeability, and magnetic susceptibility.
5. The magnetic field created by a magnetic dipole and the torque experienced by a dipole in a uniform magnetic field.
This document discusses various topics related to magnetism including:
1. The properties of bar magnets such as aligning along north-south, opposite poles attracting and like poles repelling.
2. Magnetic dipoles including current loops and solenoids behaving similarly to bar magnets with north and south poles.
3. Earth's magnetic field having a magnetic axis inclined to its geographic axis, with declination and dip angles defining their relationship.
This document discusses various topics related to magnetism including:
1. The properties of bar magnets such as having two poles and aligning along the north-south direction.
2. Current loops and solenoids acting as magnetic dipoles with a magnetic dipole moment.
3. Coulomb's law for magnetism describing the force between magnetic poles.
4. Key terms such as magnetic field strength, magnetic flux, permeability, and susceptibility.
5. The magnetic field created by a magnetic dipole and the torque experienced by a dipole in a uniform magnetic field.
This document discusses the history and key concepts of magnetism. Some of the main points covered include:
- The first known magnets were naturally occurring lodestones. Pierre de Maricourt mapped the magnetic field of a lodestone in 1263 and discovered that magnets have north and south poles.
- In the 19th century, scientists such as Faraday, Maxwell, and Henry discovered relationships between electricity and magnetism and that changing magnetic fields can induce currents in conductors.
- All magnets have magnetic dipoles with north and south poles. While electric charges can be isolated, magnetic monopoles have not been observed to exist independently.
- 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.
The document provides a history of magnetism and discoveries about magnetic fields. It discusses:
- Early uses of magnets dating back to 13th century BC by Chinese and Greeks
- Pierre de Maricourt's discovery of magnetic poles in 1269
- Connections made between electricity and magnetism from 1819-1820s
- Every magnet has two poles (north and south) that exert attractive or repulsive forces
- Magnetic field lines can be traced around magnets and charges using compasses or iron filings
- Charged particles experience a force perpendicular to their velocity and the magnetic field
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.
- Antennas convert electric currents into radio waves and vice versa. They are used in various technologies including radio, television, mobile phones, WiFi, and radar.
- The first antennas were built in 1888 by Heinrich Hertz to transmit and receive electromagnetic waves. Modern antennas come in different types for applications like broadcasting, communications, and space exploration.
- Antennas work by using an oscillating current to generate oscillating electric and magnetic fields that propagate as radio waves. During reception, the antenna intercepts some power from incoming radio waves to produce a voltage for the receiver.
This project report summarizes the construction of a 5 volt DC voltage regulator circuit using common electronic components like the LM7805 voltage regulator IC, a step-down transformer, diodes, capacitors and resistors. The circuit works by stepping down the 220V AC input voltage using the transformer. The rectified DC output is filtered and regulated by the 7805 IC to provide a stable 5V DC output. Detailed descriptions and specifications of the key components used in the circuit like the transformer, regulator IC, diodes and capacitors are provided.
The document discusses different number systems including decimal, binary, octal, and hexadecimal. It defines the base of a number system as the number of digits used. To convert between systems, integers are divided successively by the new base until the quotient is zero, while fractions and exponents are multiplied successively by the new base until the fractional part is zero. Common number systems include decimal with base 10 using digits 0-9, binary with base 2 using digits 0-1, octal with base 8 using digits 0-7, and hexadecimal with base 16 using digits 0-9 and A-F.
This document discusses phasor diagrams which are diagrams that use phasors to represent the amplitude and phase of sinusoidal quantities. Phasor diagrams allow engineers to add vectors that represent voltages and currents to show their relationship and calculate power. They provide a simple geometric method to analyze AC circuits and understand relationships between voltage, current, and power in sinusoidal steady state conditions.
This document discusses dynamic memory allocation and linked lists. It describes functions like malloc, calloc, free, and realloc for allocating and releasing memory at runtime. It also explains the concepts of linked lists, where each node contains data and a pointer to the next node, allowing flexible growth and rearrangement but slower random access than arrays.
This document discusses file input/output (I/O) operations in C programming. It covers opening, closing, reading from and writing to files. Specific file I/O functions covered include fopen(), fclose(), getc(), putc(), getw(), putw(), fprintf(), fscanf(), feof(), ferror(), fseek(), ftell(), and rewind(). Error handling during file I/O and random access to files using functions like fseek() are also discussed. Examples are provided to demonstrate reading integer and mixed data types from files and writing data to files.
Pointer is a variable that holds the address of another variable. Pointers are useful for accessing variables outside functions, efficiently handling data tables, reducing program length/complexity, and increasing execution speed. Pointers are declared with a data type followed by an asterisk and can be initialized by assigning the address of a variable. The value at a pointer's address is accessed with an asterisk. Pointers can access elements in arrays and strings. They can also access members of structures. Pointers provide a flexible way to handle one and two dimensional arrays as well as strings of varying lengths.
Structures allow grouping of related data types together under one name. A structure defines members of different data types. Structure variables can be declared to access members using dot operator. Arrays of structures can be defined to represent multiple records. Structures can be nested by defining a structure as a member of another structure. Unions are similar to structures but share same memory space for members rather than each occupying own space like in structures.
User-defined functions allow programmers to break programs into smaller, reusable parts. There are two types of functions: built-in functions that are predefined in C like printf() and user-defined functions created by the programmer. A function is defined with a return type, name, and parameters. Functions can call other functions and be called from main or other functions. Parameters can be passed by value, where the value is copied, or by reference, where the address is passed so changes to the parameter are reflected in the caller. Functions allow for modularity and code reuse.
This document discusses handling character strings in C. It describes declaring string variables as character arrays with size equal to maximum length plus one for null character. Strings can be read using scanf with %s and written using printf with %s. Common string functions are described, including strcat to concatenate strings, strcmp to compare strings, strcpy to copy strings, and strlen to determine string length.
The document discusses arrays in C programming. It defines an array as a group of related data items that share a common name, with each item indicated by an index number. One-dimensional arrays can be represented with a single subscript, while multi-dimensional arrays use multiple subscripts to reference elements by row and column. The document also covers declaring, initializing, and accessing arrays, including examples of one-dimensional, two-dimensional, and multi-dimensional arrays in C.
Looping statements allow tasks to be repeated. The three main types are for, while, and do-while loops. For loops initialize and increment a counter variable. While loops test a condition and repeat until false. Do-while loops execute the body first and then test the condition, repeating until false. Loops are useful for tasks like adding numbers in a range or printing patterns.
The document discusses different control statements in C including if, switch, and goto statements. It describes the basic syntax and usage of simple if statements, if/else statements, nested if/else statements, else if ladders, and switch statements. Key details include that if statements control program flow based on conditions, switch statements allow multi-way decisions by comparing an expression to case values, and break statements in switch cases determine where control transfers after each block.
This document discusses operators and expressions in C programming. It defines operators as symbols that tell the computer to perform mathematical or logical manipulations. It categorizes C operators and describes the meaning and usage of arithmetic, relational, logical, assignment, increment/decrement, conditional, and bitwise operators. It also discusses expressions, operator precedence and associativity, and type conversion in expressions.
This document discusses constants, variables, and data types in C programming. It defines tokens and keywords as the basic units, and explains constants and variables as values that either remain fixed or can change. Various data types are covered, including primary, user-defined, and derived types, along with modifiers that alter storage capacity. Rules for variable names and declarations are provided. The document also discusses assigning values to variables through constants, multiple assignments, and initialization.
The document provides an overview of basic computer hardware components. It discusses the central processing unit (CPU), memory units, input/output devices, storage devices like hard disk drives, optical drives, and peripherals. It also covers the motherboard, bus architecture, and factors that affect processing speed such as registers, RAM, the system clock, cache memory, and the bus. Printers, monitors, video cards, modems, network interface cards, air conditioners, uninterruptible power supplies, and RAID devices are also briefly described.
An operating system manages all the hardware and software on a computer system. It controls files, devices, memory, processing time, user access, and executes commands or provides error messages. An operating system provides an environment for other programs to do useful work, similar to a government. It consists of subsystem managers that monitor resources, enforce policies on resource allocation and deallocation.
1) Alternating current (AC) refers to sinusoidal voltage and current waveforms. AC can be generated from sources like AC generators, wind turbines, hydroelectric power plants, and solar panels.
2) Key characteristics of AC waveforms include instantaneous value, peak amplitude, peak value, peak-to-peak value, period, frequency, phase, and whether they are periodic.
3) Sinusoidal waves can be expressed as v = Vm sin(ωt+θ), where Vm is the peak amplitude, ω is the angular frequency, t is time, and θ is the phase. The phase relationship between two sinusoidal waves indicates whether one leads or lags the other.
1) An RC circuit contains a resistor and capacitor in series. The charge on the capacitor and current through the circuit can be expressed as exponential functions of time, with the time constant τ=RC.
2) For an RL circuit, the current through the inductor is expressed as 1-e^(-t/τ) where τ=L/R. This shows the current rising exponentially towards its maximum value.
3) In an RLC circuit, the charge on the capacitor undergoes damped harmonic oscillations expressed as e^(-Rt/2L)cos(ωdt), where ωd is the angular frequency of oscillations.
The document discusses the history and properties of magnetism and magnetic fields. It provides key details:
- Magnets were used in China as early as 1300 BC and the Greeks knew of magnetism by 800 BC.
- In the 13th century, French scientist Pierre de Maricourt showed that magnets have two poles: north and south. The poles are named based on their alignment with the Earth's magnetic field.
- Magnetic fields are generated by moving electric charges. The magnetic force on a charged particle depends on the particle's velocity and the magnetic field strength and direction.
- In 1819, Danish physicist Hans Christian Oersted discovered that electric currents generate magnetic fields, laying the foundation for
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spot a liar (Haiqa 146).pptx Technical writhing and presentation skills
Magnetism 1
1. Prepared by
Md. Amirul Islam
Lecturer
Department of Applied Physics & Electronics
Bangabandhu Sheikh Mujibur Rahman Science &
Technology University, Gopalganj – 8100
2.
3. Many historians of science believe that the compass, which uses
a magnetic needle, was used in China as early as the 13th
century B.C., its invention being of Arabic or Indian origin.
The early Greeks knew about magnetism as early as 800 B.C.
They discovered that the stone magnetite (Fe3O4) attracts pieces
of iron.
Legend ascribes the name magnetite to the shepherd Magnes,
the nails of whose shoes and the tip of whose staff stuck fast to
chunks of magnetite while he pastured his flocks.
Frenchman Pierre de Maricourt shows through experiments
that every magnet, regardless of its shape, has two poles, called
north pole and south pole.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.0, Page – 905
4. The poles received their names because of the way a magnet
behaves in the presence of the Earth’s magnetic field. If a bar
magnet is suspended from its midpoint and can swing freely in a
horizontal plane, it will rotate until its north pole points to the
Earth’s geographic North Pole and its south pole points to the
Earth’s geographic South Pole.
Although the force between two magnetic poles is similar to the
force between two electric charges, there is an important
difference. Electric charges can be isolated (witness the electron
and proton), whereas a single magnetic pole has never been
isolated. That is, magnetic poles are always found in pairs.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.0, Page – 905
5.
6. The region of space surrounding any moving electric charge
contains a electric field as well as a magnetic field. Historically,
the symbol B has been used to represent a magnetic field. The
direction of B at any location is the direction in which a compass
needle points at that location.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.1, Page – 906
We can define a magnetic field B at some point in space in terms
of the magnetic force FB that the field exerts on a test object, for
which we use a charged particle moving with a velocity v. From
experimental result we get that:
The magnitude FB of the magnetic force exerted on the particle
is proportional to the charge q and to the speed v of the particle.
7. The magnitude and direction of FB depend on the velocity of the
particle and on the magnitude and direction of the magnetic
field B.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.1, Page – 906
When a charged particle moves parallel to the magnetic field
vector, the magnetic force FB acting on the particle is zero.
8. When the particle’s velocity vector makes any angle θ≠0, with
the magnetic field, the magnetic force acts in a direction
perpendicular to both v and B; that is, FB is perpendicular to
the plane formed by v and B as shown on the figure left.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.1, Page – 906
9. The magnetic force exerted on a positive charge is in the
direction opposite the direction of the magnetic force exerted on
a negative charge moving in the same direction as shown on the
figure right.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.1, Page – 906
10. The magnitude of the magnetic force FB exerted on the moving
particle is proportional to sinθ, where θ is the angle the
particle’s velocity vector makes with the direction of B.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.1, Page – 906
11. We can summarize these observations by writing the magnetic
force in the form,
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.1, Page – 906
Following figure shows the right-hand rule for determining the
direction of the cross product v×B
You point the four fingers of
your right hand along the
direction of v with the palm
facing B and curl them toward
B. The extended thumb, which
is at a right angle to the fingers,
points in the direction of v×B. If
the charge is negative, the
direction of FB is opposite to the
thumb direction.
12.
13. The electric force acts in the direction of the electric field,
whereas the magnetic force acts perpendicular to the magnetic
field.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.1, Page – 909
The electric force acts on a charged particle regardless of
whether the particle is moving, whereas the magnetic force acts
on a charged particle only when the particle is in motion.
The electric force does work in displacing a charged particle,
whereas the magnetic force associated with a steady magnetic
field does no work when a particle is displaced.
14.
15. SI unit of magnetic field is the newton per coulomb-meter per
second, which is called the tesla (T):
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.1, Page – 909
Because a coulomb per second is defined to be an ampere, we
see that:
A non-SI magnetic-field unit in common use, called the gauss
(G), is related to the tesla through the conversion: 1T = 104G.
16. Example of some magnetic field and their field magnitude:
Reference: Physics II by Robert Resnick and David Halliday, Table – 29.1, Page – 910
17.
18. A charge moving with a velocity v in the presence of both an
electric field E and a magnetic field B experiences both an
electric force qE and a magnetic force qv×B. The total force
acting on the charge is then,
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.5, Page – 922
This force is called Lorentz Force.
22. A current-carrying wire also experiences a force when placed in
a magnetic field as because current is a collection of many
charged particles in motion. The resultant force exerted by the
field on the wire is the vector sum of the individual forces
exerted on all the charged particles making up the current.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.2, Page – 910
(a) A wire suspended
vertically between the poles
of a magnet. (b) the
magnetic field (blue crosses
signs) is directed into the
page. When there is no
current in the wire, it
remains vertical. (c) When
the current is upward, the
wire deflects to the left. (d)
When the current is
downward, the wire deflects
to the right.
23. Let us consider a straight segment of wire of length L and cross-
sectional area A, carrying a current I in a uniform magnetic
field B, as shown in Figure. The magnetic force exerted on a
charge q moving with a drift velocity vd is qv×B. If n is the
number of charge per unit volume then total charge on that
section of conductor is nAL.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.2, Page – 910
Thus, total magnetic force,
As, I = nqvdA thus,
24. where L is a vector that points in the direction of the current I and has
a magnitude equal to the length L of the segment. This expression is
for a straight wire in a uniform magnetic field.
Reference: Physics II by Robert Resnick and David Halliday, Topic – 29.2, Page – 910
If the wire is not straight as shown in the figure, we divide the wire
into infinitesimal segments with length ds. Thus, force exerted on a
small segment of vector length ds is,
Total force on the wire will be,
where a and b represent the end points of the wire.
30. Reference: Physics II by Robert Resnick and David Halliday, Topic – 30.1, Page – 938
In 1819, Oersted discovered that a current-carrying conductor
produces a magnetic field deflects compass needle.
(a) When no current is present in the wire, all compass needles point in the same
direction (toward the Earth’s north pole). (b) When the wire carries a strong
current, the compass needles deflect in a direction tangent to the circle, which is the
direction of the magnetic field created by the current. (c) Circular magnetic field
lines surrounding a current-carrying conductor, displayed with iron filings.
31.
32. Reference: Physics II by Robert Resnick and David Halliday, Topic – 30.1, Page – 938
In 1819 Oerested discovered that a compass needle is deflected by a
current-carrying conductor due to the magnetic field associated with
the current. After that Jean-Baptiste Biot and Félix Savart did an
experiment and arrived at a mathematical expression that gives the
magnetic field B at some point in space in terms of the current that
produces the field.
33. Reference: Physics II by Robert Resnick and David Halliday, Topic – 30.1, Page – 938
(a) The magnetic field dB at point P due to the current I through a length
element ds is given by the Biot–Savart law. The direction of the field is
out of the page at P and into the page at P’ (b) The cross product ds× 𝒓
points out of the page when 𝒓 points toward P (c) The cross product ds× 𝒓
points into the page when 𝒓 points toward P’
34. Reference: Physics II by Robert Resnick and David Halliday, Topic – 30.1, Page – 938
That expression is based on the following experimental observations
for the magnetic field dB at a point P associated with a length element
ds of a wire carrying a steady current I as shown in figure:
The vector dB is perpendicular both to ds (which points in the
direction of the current) and to the unit vector 𝒓 directed from ds to P.
35. Reference: Physics II by Robert Resnick and David Halliday, Topic – 30.1, Page – 938
The magnitude of dB is inversely proportional to r2, where r is the
distance from ds to P.
The magnitude of dB is proportional to the current I and to the
magnitude ds of the length element ds.
36. Reference: Physics II by Robert Resnick and David Halliday, Topic – 30.1, Page – 938
The magnitude of dB is proportional to sinθ, where θ is the angle
between the vectors ds and 𝒓
37. Reference: Physics II by Robert Resnick and David Halliday, Topic – 30.1, Page – 938
Thus, we can summarize the observations as,
where µ0 is a constant called the permeability of free space:
dB in above equation is the field created by the current in only a small
length element ds of the conductor. To find the total magnetic field B
created at some point by a current of finite size conductor, we must
sum up contributions from all current elements Ids that make up the
current.
38.
39.
40. Reference: Physics II by Robert Resnick and David Halliday, Example – 30.1, Page – 940
Consider a thin, straight finite length wire carrying a constant
current I and placed along the x axis as shown in Figure.
Determine the magnitude and direction of the magnetic field at
point P due to this current.
Let, point P is at a perpendicular
distance a from the wire.
A small section ds is at a distance
x from the origin on the direction
of negative x-axis.
r is the distance from point P to
ds. We consider a unit vector 𝐫
from ds to P.
Magnitude of ds vector is dx.
41. Reference: Physics II by Robert Resnick and David Halliday, Example – 30.1, Page – 940
Direction of ds is on the direction
of positive charge flow that is
current direction.
The direction of B at point P will
be out of the page, as because
ds × 𝐫 directs to the outward
direction of the page. This
direction is not depending on the
position of ds. If we consider a
unit vector k on this outward
direction, then,
42. Reference: Physics II by Robert Resnick and David Halliday, Example – 30.1, Page – 940
According to Biot-Savart law, we
get,
As we now know that the
direction of B is toward k vector,
we now calculate the magnitude.
For determining total B we have to integrate the expression.
Before that, we have to express the variables r and x in terms of θ.
43. Reference: Physics II by Robert Resnick and David Halliday, Example – 30.1, Page – 940
Now, sinθ =
a
r
or, r = a cosecθ
and, tanθ =
a
−x
or, x = - a cotθ
thus, dx = a cosec2θ dθ
Putting these values on the
previous expression, we get,
** If we considered the section ds on positive x-axis, the result would be same
because the angle θ for positive x-axis is greater than 90°.
44. Reference: Physics II by Robert Resnick and David Halliday, Example – 30.1, Page – 940
Now, we can integrate the
expression within the limit θ1 and
θ2 as shown in figure.
This is the expression of B for a
finite length current carrying wire.
Special Case:
If the wire is infinitely long then θ1 = 0° and θ2 = 180°. Thus,
cos 0° – cos 180° = 2 and then,
45.
46. Reference: Physics II by Robert Resnick and David Halliday, Example – 30.2, Page – 943
Later
47.
48. Reference: Physics II by Robert Resnick and David Halliday, Example – 30.1, Page – 940
The line integral of B.ds around any closed path equals µ0I.
Where I is the total continuous current passing through any
surface bounded by the closed path.
For a straight wire as shown in
figure, the field lines are circular
around the wire. If we consider
such a closed circular path with
radius r, on every point on that
path magnitude of B will be
same. If we slice that path into
infinitesimal ds sections, for
every section the angle between
ds and B will be 0°.
49. Reference: Physics II by Robert Resnick and David Halliday, Example – 30.1, Page – 940
Thus we get,
Here, magnitude of B is constant on that path and 𝒅𝒔 is the
circumference 2πr. This expression is called Ampere’s Law.
** We can compare this equation with Gauss’s law, ε0 𝑬. 𝒅𝒔 = qin