Question
State Faraday’s law of electromagnetic induction. Explain Lenz’s law and show how it is consistent with the law of conservation of energy. Give two examples.
(NCERT Class 12, Chapter 6)
Solution — Step by Step
Faraday’s law: The magnitude of the induced EMF in a circuit is equal to the rate of change of magnetic flux through the circuit.
For a coil with turns:
The negative sign comes from Lenz’s law.
Lenz’s law: The direction of the induced current is such that it opposes the change in magnetic flux that produced it.
The word “opposes” is crucial — the induced current doesn’t oppose the flux itself, but the change in flux. If flux is increasing, the induced current creates a magnetic field to decrease it. If flux is decreasing, the induced current tries to maintain it.
If the induced current aided the change (instead of opposing it), the flux would change even faster, inducing a larger current, which would further increase the flux — a runaway process creating energy from nothing. This would violate conservation of energy.
By opposing the change, the induced current requires an external agent to do work against this opposition. This work is the source of the electrical energy produced. Energy is conserved.
When the north pole of a magnet moves towards a coil, the flux through the coil increases. By Lenz’s law, the induced current flows in a direction that creates a north pole facing the magnet — repelling it. You must push harder (do work) to move the magnet closer.
When a rectangular loop is pulled out of a uniform magnetic field, the flux decreases. The induced current flows in a direction that tries to maintain the flux (by creating a field in the same direction as the external field inside the loop). This current in the magnetic field experiences a force that opposes the pulling — you must exert force to pull it out.
Why This Works
Faraday’s law connects a mechanical/magnetic change to an electrical effect. The negative sign (Lenz’s law) is nature’s way of enforcing energy conservation in electromagnetic phenomena. Every generator, transformer, and induction cooktop works on this principle.
The induced EMF depends on how fast the flux changes, not on the magnitude of flux itself. A strong constant field produces no EMF — only changing flux matters.
Alternative Method — Using Motional EMF
For a conductor of length moving with velocity in a field :
This is a special case of Faraday’s law where the flux changes because the area of the circuit changes. Both approaches give the same answer.
In NEET and CBSE, always use the right-hand rule or the flux change approach to determine the direction of induced current. For JEE, the motional EMF formula is faster for problems involving sliding rods on rails.
Common Mistake
Students often write that the induced current “opposes the magnetic flux.” This is wrong. It opposes the change in flux. If the flux is decreasing, the induced current actually acts to support the existing flux (not oppose it). Always ask: is flux increasing or decreasing? Then oppose that change.