Electromagnetic induction
Michael Faraday and Joseph Henry found that a changing magnetic flux through a circuit produces an emf in it. This is electromagnetic induction.
Magnetic flux through an area A is Φ = BA cos θ, where θ is the angle between B and the normal to the area. Unit: weber (Wb) = T m².
Faraday’s law: the induced emf equals the rate of change of magnetic flux linkage: ε = –N dΦ/dt. The flux can change by changing B, the area, or the angle (rotation).
Lenz’s law: the direction of the induced current is such that it opposes the change in flux that causes it. This is shown by the minus sign in Faraday’s law. Lenz’s law is a consequence of the conservation of energy: if the induced current helped the change, energy would be created from nothing. For example, when the north pole of a magnet is pushed towards a coil, the near face of the coil becomes a north pole and repels the magnet.
Motional emf: a rod of length l moving with speed v perpendicular to a field B has emf ε = Blv across its ends.
Eddy currents: changing flux induces loops of current inside bulk metal pieces. They cause heating and energy loss (reduced by laminating cores) but are useful in electromagnetic damping, induction furnaces and magnetic brakes in trains.
Worked example: a 100-turn coil’s flux falls from 0.05 Wb to 0.01 Wb in 0.2 s. ε = 100 × 0.04/0.2 = 20 V.
Key points
- Φ = BA cos θ; 1 Wb = 1 T m².
- ε = –N dΦ/dt; ε = Blv.
- Lenz’s law → conservation of energy.
- Eddy currents are reduced by laminated cores.
Exam tips
- Use change in flux ÷ time; ignore the sign when asked for magnitude.
- For direction questions, think: “the coil opposes the change”.
Common mistakes
- Thinking a large but constant flux produces emf; only a changing flux does.
- Linking Lenz’s law to charge conservation instead of energy conservation.
- Forgetting N in a multi-turn coil.