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Lenz's Law and Energy Conservation

Lenz's law states that the direction of induced current is such that its magnetic effect opposes the change in magnetic flux that produces it.

In one line: Lenz says nature resists the change, not the field label.

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Understand it

  • Lenz's law is the direction rule for induced current.
  • If flux through a coil increases, the induced current produces a magnetic field opposing that increase.
  • If flux decreases, the induced current acts to support the original flux.
  • This opposition is necessary for conservation of energy because external work is required to maintain the change.

Example

When the north pole of a magnet approaches a coil, the near face of the coil behaves like a north pole to oppose the approach. Work must be done against this repulsion, and that work appears as electrical energy and heat in the circuit.

Formula and rule

Rule: The negative sign in epsilon = -dPhiB/dt represents Lenz's law.

It is a sign convention showing that induced emf acts against the change in flux.

Here epsilon is induced emf, PhiB is magnetic flux, and t is time.

Lenz's law does not change the magnitude formula; it fixes the physically correct direction of induced emf or induced current.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A conducting rod of length 0.50 m moves to the right at 4.0 m s−1 on rails in a uniform magnetic field of 0.20 T directed into the page.

  1. 1The flux into the rail loop increases, so by Lenz's law the induced current must produce a field out of the page to oppose that increase.
  2. 2Hence the induced current is anticlockwise.
  3. 3The emf magnitude is epsilon = Bvl = 0.20 × 4.0 × 0.50 = 0.40 V.
  4. 4If the circuit resistance is 2.0 ohm, I = epsilon/R = 0.40/2.0 = 0.20 A.
  5. 5The magnetic force on the rod is opposite to its motion, so an external force must do work to keep it moving uniformly.

Method you can reuse

  1. 1Assumptions for direction derivation: consider a closed conducting circuit, a changing magnetic flux, and induced current small enough that its effect is described by its magnetic field.
  2. 2Key steps: identify the original flux direction, decide whether that flux is increasing or decreasing, choose the induced magnetic field that opposes only the change, and then use the right-hand grip rule to obtain current direction.
  3. 3Final result cue: induced current always acts so that external work is needed to maintain the flux change, preserving energy conservation.

Visual tip

A magnet-coil diagram is helpful. Mark the approaching or receding pole, original magnetic field through the coil, whether flux increases or decreases, and the induced pole face of the coil.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why does Lenz's law support conservation of energy?

Think first, then show answer
Lenz's law supports conservation of energy because the induced current opposes the change causing it. Therefore, an external agent must do work to change the flux, and this work is converted into electrical energy or heat instead of appearing from nowhere.

Common wrong answer

Choosing current direction so that it attracts the approaching magnet and increases the cause of induction, which would violate energy conservation.

Don't mix this up

Students often say induced current opposes the magnetic field itself. More precisely, it opposes the change in magnetic flux, not necessarily the original field.

Exam tip

For direction questions, first decide whether flux is increasing or decreasing, then choose the induced magnetic field that opposes that change.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

It appears in assertion-reason questions, direction of induced current problems, and short answers asking why induced current cannot aid the motion that produces it.
  1. 1

    Enough for 1 mark

    Lenz's law states that the direction of induced current is such that its magnetic effect opposes the change in magnetic flux that produces it.

  2. 2

    Add for 2 marks

    Example: When the north pole of a magnet approaches a coil, the near face of the coil behaves like a north pole to oppose the approach. Work must be done against this repulsion, and that work appears as electrical energy and heat in the circuit.

  3. 3

    Add for 3 marks

    Lenz's law is the direction rule for induced current.

Practice

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