Question
State Lenz’s law and explain, from first principles, why the induced current must oppose the change in magnetic flux. Why does Lenz’s law reflect conservation of energy?
Solution — Step by Step
Lenz’s law: The induced current in a conductor is in such a direction that the magnetic field it creates opposes the change in magnetic flux that produced it.
More compactly: the induced effect always opposes its cause.
Quantitatively, this is captured by the negative sign in Faraday’s law:
The minus sign IS Lenz’s law — it tells us that the EMF is induced in the direction that opposes the rate of change of flux.
Consider a bar magnet’s north pole approaching a conducting coil. As it approaches:
- Magnetic flux through the coil increases
- By Faraday’s law, an EMF is induced
- By Lenz’s law, the induced current must create a magnetic field that OPPOSES the increase in flux
How to oppose the increase? By creating a magnetic field pointing AWAY from the approaching north pole — i.e., the face of the coil facing the magnet must act as a north pole (repelling the magnet).
Using the right-hand rule, this tells us the direction of induced current. If the magnet is pulled away (flux decreases), the induced current reverses direction to attract the magnet (opposing the decrease).
Memory device: Lenz’s law always makes the system “fight back.” If something changes, the system tries to resist that change.
This is the “why” that separates a thorough answer from a superficial one.
Suppose (hypothetically) the induced current AIDED the change instead of opposing it. If you brought a magnet near a coil and the induced current attracted the magnet (rather than repelling it):
- The magnet would accelerate toward the coil (aided by attraction)
- This increasing approach would induce more current
- More current would create stronger attraction
- Even stronger attraction → faster approach → even more current…
The system would accelerate indefinitely, creating energy from nothing. This violates conservation of energy.
Therefore, for energy to be conserved, the induced current MUST oppose the change. You must do work against the opposing force to maintain the change in flux — that work done is what provides the electrical energy to the circuit. There is no free lunch: you get electrical energy out only because you do mechanical work in.
When a conducting rod moves with velocity on rails in a magnetic field :
- Induced EMF: (where = length of rod)
- Induced current:
- Force on the current-carrying rod: (opposing the motion, per Lenz’s law)
- Power dissipated in resistance:
- Power of external agent doing work:
These are equal — all the mechanical work done is converted to electrical energy (heat in the resistor). Conservation of energy is perfectly satisfied.
This braking effect is used in eddy current brakes (maglev trains, electromagnetic braking in heavy vehicles).
Why This Works
Lenz’s law is not an independent law — it is a consequence of Faraday’s law combined with energy conservation. The negative sign in is not arbitrary; it is forced upon us by the requirement that electromagnetic induction cannot violate conservation of energy.
This makes Lenz’s law deeper than it first appears. It’s not just a rule to find current direction — it’s a statement about the fundamental nature of electromagnetic induction as an energy conversion process.
Alternative Method
Lenz’s law via flux rule (for circuits):
- If flux is increasing → induced current creates a field opposing the original B → the induced field points in the direction opposite to the external B
- If flux is decreasing → induced current creates a field in the same direction as the external B (trying to maintain flux)
Decide the direction of induced B first (using Lenz’s logic), then use the right-hand rule to find the direction of induced current. This two-step approach is faster in MCQ problems.
Common Mistake
The most common error is applying Lenz’s law as “the induced current opposes the external magnetic field.” This is wrong. It opposes the change in flux. If flux is increasing, the induced field opposes the increase (opposes external field). If flux is decreasing, the induced field supports the field (acts in the same direction as external B). The induced current’s direction depends on whether flux is increasing or decreasing, not on the direction of the external field itself.
Lenz’s law questions in JEE often give you a situation (coil falling through a field region, conducting ring near a wire with increasing current, etc.) and ask you to find the direction of induced current or whether the force is attractive or repulsive. The reliable method: (1) determine if flux through the conductor is increasing or decreasing; (2) induced B must oppose that change; (3) use right-hand rule to find induced current direction; (4) use to find the mechanical force direction.