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What is Faraday's law of electromagnetic induction?

Class 12 PhysicsNCERT chapter: Electromagnetic Inductionइसे हिंदी में पढ़ें

Exam-ready answer

Faraday's law of electromagnetic induction states that the magnitude of the emf induced in a circuit is equal to the time rate of change of magnetic flux through it: ε = −dΦB/dt. For a coil of N closely wound turns, ε = −N dΦB/dt. The negative sign shows the direction of the emf, given by Lenz's law.

Explanation

In Faraday's experiments a coil is connected to a galvanometer. When a bar magnet is pushed towards the coil, the galvanometer deflects; when the magnet is pulled away, it deflects the other way; when the magnet is held still, there is no deflection. A faster movement gives a larger deflection. The same happens when a second, current-carrying coil is moved, or when its current is switched on or off.

The common cause in all these cases is a change in the magnetic flux linked with the coil. Flux through a plane area A in a uniform field B is ΦB = B·A = BA cos θ, where θ is the angle between B and the area vector. Its SI unit is the weber (Wb), where 1 Wb = 1 T m². An emf is induced only while the flux is changing, not merely because it is large.

Flux can be changed in three ways: by changing B, by changing the area A of the coil inside the field, or by changing the angle θ. An electric generator uses the third method: a coil rotates in a magnetic field, θ changes continuously, the flux keeps changing and an alternating emf is induced. The faster the rotation, the greater the rate of change of flux and the larger the emf.

Points to remember

  1. Induced emf ε = −dΦB/dt; for N turns, ε = −N dΦB/dt.
  2. Magnetic flux ΦB = BA cos θ; SI unit weber (Wb), 1 Wb = 1 T m².
  3. An emf is induced only while the flux linked with the circuit changes.
  4. Flux can change through a change in B, in area A, or in orientation θ.
  5. The negative sign expresses Lenz's law: the induced emf opposes the change in flux.

Exam tip

Write ε = −N dΦB/dt and define flux as ΦB = BA cos θ with its unit, the weber. In experiment-based questions, describe the galvanometer deflection for the magnet moving in, moving out and held still.

Questions students also ask

Why is no current induced when the magnet is held still inside the coil?
Induced emf depends on the rate of change of flux, not on the flux itself. When the magnet is stationary, the flux through the coil is constant, so dΦB/dt = 0 and no emf or current is induced, even though the field is strong.
How can the induced emf in a coil be increased?
Increase the rate of change of flux. This can be done by moving the magnet faster, using a stronger magnet, increasing the number of turns N, or increasing the area of the coil. Each of these raises N dΦB/dt and so raises the emf.
What is the difference between induced emf and induced current?
An emf is induced whenever the flux changes, even if the circuit is open. A current flows only when the circuit is closed, and its value is the induced emf divided by the total resistance of the circuit, I = ε/R.

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