Faraday's and Lenz's laws

MDCAT Physics · Physics · Electromagnetic induction. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

Magnetic flux through a loop is the flux density multiplied by the area that the field passes through at right angles. An EMF is induced in a circuit whenever the flux linking it changes: the field may change, the area may change, or the coil may turn. Faraday's law says that the size of the EMF equals the rate of change of flux linkage. A steady flux, however large, induces nothing.

Lenz's law gives the direction: the induced current flows so that its own magnetic effect opposes the change that causes it. This is the conservation of energy. Work must be done against the opposing force, and that work becomes electrical energy.

Rules to remember

Common mistake

Using the angle between the field and the plane of the loop in Φ = BA cos θ. The angle θ is measured from the normal, so a field at 30° to the plane means θ = 60°.

Worked example

The flux through each turn of a 200-turn coil falls steadily from 6.0 × 10−3 Wb to 2.0 × 10−3 Wb in 0.10 s. What is the size of the induced EMF?

  1. Change in flux per turn ΔΦ = (6.0 − 2.0) × 10−3 = 4.0 × 10−3 Wb.
  2. EMF = N × ΔΦ ÷ Δt = 200 × 4.0 × 10−3 ÷ 0.10.
  3. = 0.80 ÷ 0.10 = 8.0 V.

Answer: 8.0 V

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