Electromagnetic induction: study guide

Key ideas

A changing magnetic flux through a loop induces an emf. Faraday’s law gives its size, Lenz’s law gives its direction, and the same idea explains generators, transformers and inductors.

• Faraday’s law is ε = −N ΔΦ ÷ Δt, where the flux is Φ = BA cos θ. Only a change in flux induces an emf.
• Lenz’s law, the minus sign, says the induced current opposes the change that produced it.
• A conductor of length L moving at speed v across a field has a motional emf of BLv.
• An inductor stores energy ½LI² in its magnetic field, and it resists changes in current.

Key equations

• ε = −N ΔΦ ÷ Δt
• Φ = BA cos θ
• ε = BLv (motional)
• ε = NBAω sin ωt (generator)
• U = ½LI²
• L = μ₀N²A ÷ ℓ (solenoid)

Worked example

A rod 0.50 m long slides at 4.0 m/s perpendicular to a 0.20 T field on rails that form a 2.0 Ω circuit. The emf is BLv = 0.20 × 0.50 × 4.0 = 0.40 V and the current is 0.40 ÷ 2.0 = 0.20 A. The magnetic force opposing the motion is BIL = 0.20 × 0.20 × 0.50 = 0.020 N, so the power needed is 0.020 × 4.0 = 0.080 W, equal to I²R.

Common mistakes

• Forgetting the number of turns N when the coil has many windings.
• Using the flux itself instead of its rate of change. A constant flux induces nothing.
• Ignoring Lenz’s law when finding the direction of the induced current.

Practice

Test yourself with practice questions on this topic: Electromagnetic induction