Inducing an e.m.f.
Electromagnetic induction is the production of an induced e.m.f. in a conductor when there is a change in the magnetic field around it. If the conductor forms a complete circuit, an induced current flows. An e.m.f. is induced when a straight wire is moved across a magnetic field, or when the magnetic flux through a coil changes — for example by pushing a magnet in or out of the coil.
Faraday's and Lenz's laws
Faraday's law states that the size of the induced e.m.f. is directly proportional to the rate of change of magnetic flux. So the e.m.f. is larger if the magnet moves faster, the field is stronger, or the coil has more turns.
Lenz's law gives the direction: the induced current always flows in a direction that opposes the change producing it. This is a consequence of the conservation of energy.
Key formula
Induced e.m.f. ε ∝ rate of change of flux
Factors that increase ε: faster relative motion, stronger magnet (larger B), more turns N on the coil.
Worked example
A magnet is pushed into a coil of 200 turns and the flux through each turn changes by 0.02 Wb in 0.5 s. Estimate the induced e.m.f.
Rate of change of flux per turn = 0.02 / 0.5 = 0.04 Wb s⁻¹.
For 200 turns: ε = 200 × 0.04 = 8 V.
If the magnet is pushed in twice as fast, the e.m.f. doubles to 16 V.
Remember
- No change in flux → no induced e.m.f. (a stationary magnet gives nothing).
- Fleming's RIGHT-hand rule gives the induced current direction for a moving wire.
- Lenz's law: the induced effect opposes the change that caused it.