Section 5.6: Lenz’s Law

Lenz’s Law states that the direction of the induced current in a conductor due to changing magnetic flux will be such that the magnetic field it creates opposes the change that produced it. This law ensures conservation of energy in electromagnetic systems.

Mathematical Form:
\( \mathcal{E} = - \frac{d\Phi_B}{dt} \)

The negative sign indicates the opposition of the induced EMF to the change in flux.

Lenz's Law Illustration

Example 1

A magnet is pushed towards a coil. Determine the direction of induced current according to Lenz’s Law.

The induced current creates a magnetic field opposing the approaching magnet. Thus, if the north pole approaches, the coil's near side becomes a north pole to repel it.

Example 2

A loop of wire experiences a decrease in magnetic flux. Describe the induced current direction.

The induced current will produce a magnetic field attempting to maintain the original flux, meaning it flows in a direction that reinforces the original field through the loop.

Practice Problems

  1. A coil of 100 turns is exposed to a magnetic flux decrease of 0.05 Wb in 0.02 s. Calculate induced EMF and describe current direction.
  2. Explain how Lenz's Law demonstrates conservation of energy in electromagnetic induction.
  3. A rectangular loop moves out of a uniform magnetic field. Determine induced current direction.
  4. Design a simple experiment to visualize Lenz's Law using magnets and coils.
  5. A solenoid is connected to a resistor. A bar magnet is dropped through it. Sketch EMF vs. time graph.