Induced EMF from a changing flux

What voltage does a coil see while the flux through it changes?

ε = -N \frac{ΔΦ}{Δt}

Method

1. Convert the flux change to webers and the time to seconds.
2. Divide the flux change by the time to get the average rate of change over the interval — this is what dΦ/dt means for a real, discrete measurement rather than an instantaneous one.
3. Multiply by the number of turns: each turn contributes its own share of the same changing flux, and the coil sees the sum.
4. The minus sign is Lenz's law — the induced EMF opposes the change that made it — and only matters once a sign convention for the flux change has been chosen. The magnitude is what sizes the winding.

Assumptions

• The rate of change is treated as constant over the interval. A real pulsed field changes fastest at the edges of the pulse, so this is the average EMF, not the peak — a sharper edge gives a higher instantaneous voltage than this figure.
• Every turn links the same flux change. In a real coil, turns nearer the field source see more change than turns further out; this treats the winding as tightly bunched.
• No resistive or eddy-current loss is modelled — this is the EMF generated, not the voltage that would be measured across a loaded winding.