Electromagnetic induction

NUST NET (Engineering) · Physics · Magnetism and alternating current. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

An EMF is induced in a circuit whenever the magnetic flux through it changes. It does not matter how the change is made: moving a magnet, moving a wire, turning a coil or changing a current nearby. A steady flux, however large, induces nothing.

Faraday's law gives the size of the EMF: the rate of change of flux linkage. Lenz's law gives its direction: the induced current always opposes the change that causes it, which is conservation of energy at work.

A changing current in a coil induces an EMF in the same coil (self-induction) or in a neighbouring coil (mutual induction). Generators and transformers rely on this, so a transformer works only on AC.

Rules to remember

Common mistake

Scaling transformer current the same way as voltage. Power is unchanged in an ideal transformer, so if the voltage is stepped up 5 times the current is stepped down 5 times.

Worked example

The current in a coil of self-inductance 0.40 H falls steadily from 5.0 A to 2.0 A in 0.060 s. What is the size of the induced EMF, and which way does it act?

  1. Change in current: ΔI = 5.0 − 2.0 = 3.0 A.
  2. Rate of change: ΔI/Δt = 3.0/0.060 = 50 A s−1.
  3. EMF = L × ΔI/Δt = 0.40 × 50 = 20 V.
  4. By Lenz's law it opposes the fall, so it acts in the direction of the current and tries to keep it flowing.

Answer: 20 V, acting in the same direction as the current.

Practice questions

Try each one, then open the answer.

1. Two coils have a mutual inductance of 0.50 H. The current in the primary coil changes at 20 A s−1. The EMF induced in the secondary coil is

  1. A
    10 V
  2. B
    40 V
  3. C
    0.025 V
  4. D
    20 V
Show answer

Answer: A. εs = M ΔIp/Δt = 0.50 × 20 = 10 V. 40 V divides by M instead of multiplying.

2. Lenz's law, which gives the direction of an induced current, is a consequence of the conservation of

  1. A
    charge
  2. B
    momentum
  3. C
    energy
  4. D
    mass
Show answer

Answer: C. The induced current always opposes the change that causes it, so work must be done to produce it. If it helped the change, energy would be created from nothing.

3. An inductor of 0.20 H carries a steady current of 3.0 A. The energy stored in its magnetic field is

  1. A
    0.30 J
  2. B
    0.60 J
  3. C
    1.8 J
  4. D
    0.90 J
Show answer

Answer: D. U = ½LI2 = ½ × 0.20 × 9.0 = 0.90 J. Leaving out the ½ gives 1.8 J, and not squaring I gives 0.30 J.

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