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Faraday's Law of Electromagnetic Induction

Learn the concept

Student-friendly explanation

How to write this in exams

1
Start with the exact idea
Faraday's law states that the magnitude of induced emf in a circuit is equal to the rate of change of magnetic flux linked with the circuit. Mathematically, epsilon = - dPhi_B/dt for one turn and epsilon = -N dPhi_B/dt for N turns.
2
Then show how to use it
Find initial and final flux per turn. Calculate Delta Phi and time interval. Multiply by number of turns. Use magnitude for numerical value, then use Lenz's law if direction is asked.
3
Add one concrete example
When a bar magnet is pushed towards a coil connected to a galvanometer, the changing flux through the coil produces an induced emf and the galvanometer deflects.
4
Avoid this incomplete answer
Ignoring number of turns N or using final flux divided by time instead of change in flux divided by time.

Definition

Example

When a bar magnet is pushed towards a coil connected to a galvanometer, the changing flux through the coil produces an induced emf and the galvanometer deflects.

Rule to remember

Formula: epsilon = -N dPhi_B/dt. Here epsilon is induced emf in volt (V), N is the number of turns in the coil, Phi_B is magnetic flux through one turn in weber (Wb), t is time in second (s), and dPhi_B/dt is the rate of change of flux. The minus sign represents Lenz's law: the induced emf acts in the direction that opposes the change in flux. For magnitude in numericals, use |epsilon| = N |Delta Phi_B|/Delta t.

Memory hook

Faraday tells how much emf is induced from changing flux; the faster the flux changes and the more turns the coil has, the larger the emf. Remember: change in flux creates emf, rate of change sets its size, and Lenz's law sets its direction.

Examples and method

Worked example

A coil of 200 turns has flux through each turn changing from 3.0 x 10^-4 Wb to 1.0 x 10^-4 Wb in 0.02 s. Magnitude of induced emf = N |Delta Phi|/Delta t = 200 x |1.0 x 10^-4 - 3.0 x 10^-4| / 0.02 = 200 x 2.0 x 10^-4 / 0.02 = 2.0 V. The emf is produced because flux decreases rapidly.

Method to apply

Find initial and final flux per turn. Calculate Delta Phi and time interval. Multiply by number of turns. Use magnitude for numerical value, then use Lenz's law if direction is asked.

Diagram support

Draw a coil connected to a galvanometer and a bar magnet moving toward or away from it. Label N and S poles, direction of motion, coil, galvanometer, and induced current direction for the chosen case.

How CBSE asks it

CBSE questions often ask for the law statement, mathematical form, numerical emf calculation, or explanation of galvanometer deflection when magnet-coil motion changes.

Avoid common mistakes

Common confusion

A common mistake is to say induction occurs merely because a magnet is near a coil. A steady flux does not induce emf; the flux linkage must change with time.

Common wrong answer

Ignoring number of turns N or using final flux divided by time instead of change in flux divided by time.

Exam tip

In written answers, mention both parts: changing magnetic flux is the cause, and induced emf is proportional to the rate of change of flux.

Quick check

Why is no emf induced in a coil placed near a stationary magnet?

No emf is induced because the magnetic flux linked with the coil remains constant. Faraday's law requires a change of flux with time, so dPhi_B/dt = 0 and the induced emf is zero.

Answer writing and exam use

1-mark answer

2-mark answer

Faraday's law states that the magnitude of induced emf in a circuit is equal to the rate of change of magnetic flux linked with the circuit. Mathematically, epsilon = - dPhi_B/dt for one turn and epsilon = -N dPhi_B/dt for N turns. Formula: epsilon = -N dPhi_B/dt. Here epsilon is induced emf in volt (V), N is the number of turns in the coil, Phi_B is magnetic flux through one turn in weber (Wb), t is time in second (s), and dPhi_B/dt is the rate of change of flux. The minus sign represents Lenz's law: the induced emf acts in the direction that opposes the change in flux. For magnitude in numericals, use |epsilon| = N |Delta Phi_B|/Delta t. When a bar magnet is pushed towards a coil connected to a galvanometer, the changing flux through the coil produces an induced emf and the galvanometer deflects.

3-mark answer

An emf is induced whenever magnetic flux linked with a closed circuit changes with time. The change may happen by changing magnetic field, area, orientation, or by relative motion between a magnet and coil. The negative sign shows the direction given by Lenz's law. Formula: epsilon = -N dPhi_B/dt. Here epsilon is induced emf in volt (V), N is the number of turns in the coil, Phi_B is magnetic flux through one turn in weber (Wb), t is time in second (s), and dPhi_B/dt is the rate of change of flux. The minus sign represents Lenz's law: the induced emf acts in the direction that opposes the change in flux. For magnitude in numericals, use |epsilon| = N |Delta Phi_B|/Delta t. A coil of 200 turns has flux through each turn changing from 3.0 x 10^-4 Wb to 1.0 x 10^-4 Wb in 0.02 s. Magnitude of induced emf = N |Delta Phi|/Delta t = 200 x |1.0 x 10^-4 - 3.0 x 10^-4| / 0.02 = 200 x 2.0 x 10^-4 / 0.02 = 2.0 V. The emf is produced because flux decreases rapidly. CBSE questions often ask for the law statement, mathematical form, numerical emf calculation, or explanation of galvanometer deflection when magnet-coil motion changes. Ignoring number of turns N or using final flux divided by time instead of change in flux divided by time.

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