20.2 Faraday's Law and Flux Linkage

Real coils usually have many turns, so induction depends on total flux linkage N Phi, not just flux through one loop. If each turn sees the same flux, linkage scales directly with N. This is the first reason transformers and generators use many turns: induced emf can be increased without increasing field strength.

When a loop is partly outside a field region, only the overlapping area contributes. That means induction tasks often become geometry-plus-time problems: write area overlap as a function of time, then convert it to flux and differentiate or use finite differences.

In many IB questions you can use the average form $\epsilon_{\text{avg}} = -\Delta(N\Phi)/\Delta t$ over a known interval. For sinusoidal or continuously changing systems, instantaneous values matter and differential form is cleaner. Both are the same law, used at different resolution.

A useful exam check: if the field is static, loop area is fixed, and orientation is fixed, then flux is constant and induced emf must be zero. Students often expect current just because a field exists, but induction needs change, not just presence.