This document provides an overview of key concepts in magnetic fields and electromagnetic induction: 1. It defines magnetic fields and describes their properties such as strength and direction. Magnetic fields are generated by magnetic objects and electric currents. 2. The interactions between magnetic fields and moving electric charges or currents are explained through concepts like the Lorentz force law and right hand rules. 3. Electromagnetic induction and its governing laws discovered by Faraday and Lenz are summarized, explaining how changing magnetic fields induce electromotive forces (EMFs) in conductors. 4. Self and mutual induction are introduced, where changing currents in conductors induce opposing EMFs due to their own or neighboring conductors' magnetic fields.

1. Certificate Course
on
Techniques of Problem Solving in Physics
Magnetic Field
• A magnetic field is a vector field that describes the magnetic influence on magnetic
substance.
• The invisible area around a magnetic object that can pull another magnetic object toward
it or push another magnetic object away from it is called a magnetic field.
• Magnetic field is measured by its strength and by the direction it points.
• The strength of a magnetic field, called the magnetic flux density, is measured in units of
Tesla.
• Field lines exit the magnet at its north pole, travel around in the air, and re-enter the
magnet through its south pole.
Force acting on a charged particle in magnetic field
F
̅ = q ∙ v
̅ × B
̅
Magnetic dipole
• A magnetic dipole is a pair of equal and opposite poles separated by a small distance.
• A model of an object that generates a magnetic field in which the field is considered to
emanate from two opposite poles, as in the north and south poles of a magnet.
• Magnetic compass needles and bar magnets are examples of macroscopic magnetic
dipoles.
• The strength of a magnetic dipole, called the magnetic dipole moment, may be thought of
as a measure of a dipole’s ability to turn itself into alignment with a given external magnetic
field.
• The magnetic dipole moment, often simply called the magnetic moment, may be defined
then as the maximum amount of torque caused by magnetic force on a dipole that arises
per unit value of surrounding magnetic field in vacuum.
Magnetic effect of Electric current
• Oersted performed an important experiment which showed that there was a connection
between electricity and magnetism. When a current was switched on through a wire, it
made a compass needle turn so that it was at right angles to the wire. The current had
produced a magnetic field strong enough to cause the compass needle to turn.
• The magnitude of magnetic field increases with increase in electric current and decreases
with decrease in electric current.
• The magnitude of magnetic field produced by electric current decreases with increase in
distance and vice – versa. The size of concentric circles of magnetic field lines increases
with distance from the conductor, which shows that magnetic field decreases with
distance.
• Magnetic field lines are always parallel to each other.
• No two field lines cross each other.

2. Right-Hand Thumb Rule
If a current carrying conductor is held by right hand, keeping the thumb straight and if the
direction of electric current is in the direction of thumb, then the direction of wrapping of other
fingers will show the direction of magnetic field.
Biot Savart Law
It is an equation describing the magnetic field generated by a constant electric current. It
relates the magnetic field to the magnitude, direction, length, and proximity of the electric current.
dB =
𝜇0
4π
∙
I ∙ d𝑙 ∙ sin θ
r2
Magnetic field due to current carrying wire
B =
μ0I
2πr
Magnetic field inside current carrying solenoid
B =
Nμ0I
L
Varying Currents
Faraday's Experiments
• Coil and Magnet Experiment
• Coil and Coil Experiment
Faraday's Laws of Electromagnetic Induction:
First Law: Whenever there is a change in the magnetic flux linked with a circuit, an emf is induced
in the circuit.
Second Law: The magnitude of the induced emf is directly proportional to the rate of change of
magnetic flux through the circuit with respect to time.
Lenz’s Law:
It states that the induced emf is always in such a direction as to oppose the change in
magnetic flux that produces the induced emf.
Induced emf =
dφB
dt
Magnetic flux = B
̅ ∙ A
̅
Fleming’s right-hand rule:
Stretch the thumb and the first two fingers of the right hand, so they are mutually
perpendicular to each other. If the forefinger points the direction of magnetic field and thumb the
direction of the motion of the conductor then the middle finger points the direction of the induced
emf.

3. Self-induction:
When current is passed through a conductor it produces magnetic field. If the current
flowing through the conductor is changing, then magnetic flux set p by the current is also changing.
The changing magnetic flux induces an emf, which opposes the original change in the current.
This phenomenon is called self-induction and the induced emf is called as counter emf or back
emf.
Self-induction is defined as the emf induced in the circuit when the current in the circuit decays at
the rate of one ampere per second.
S.I. unit of self-induction is Henry.
The coil is said to have a self-inductance of one Henry if an emf of one volt is induced in it when
the current in the coil changes at the rate of one ampere one second.
Magnetic flux = LI
Mutual induction:
The phenomenon in which a change in current in one coil induces an opposing emf in a
neighborhood coil is called mutual induction.
The coefficient of mutual induction is defined as the emf induced in the secondary when
the rate of change of current in the primary is unity.
S.I. unit of coefficient of mutual induction is Henry.
The coefficient of mutual induction between two coils is one Henry if an emf of one volt is induced
in the secondary coil when the current in the primary coil changes at the rate of one ampere per
second.
Mutual induction between two coils depends upon
i. Number of turns of primary and secondary coils
ii. The geometry of the coils.
iii. The distance of separation of the coils.
iv. The permeability of the medium between the coils.