# Electromagnetic induction (finding ΔΦ).

KarlsShwarzschild

I am unsure if I understand what you are doing. It seems ##\frac{d}{\sqrt{2gh}}## is approximately the time that the magnet spends inside the coil. You are also using $$\mathcal{E} = -N\frac{d\Phi}{dt}$$I suppose the average rate of change of flux in a time ##\Delta t## is ##\frac{\Delta \Phi}{\Delta t}##, from which it follows that the average EMF ##\mathcal{E} = -N \frac{\Delta \Phi}{\Delta t}##. So your construction ##\mathcal E = -N \frac{\Delta \Phi}{d}\sqrt{2gh}## is the time-averaged EMF inside the coil whilst the magnet is inside the coil. However this is zero, because ##\frac{1}{T} \int_0^T -N\frac{d\Phi}{dt} dt = 0##, since the flux linked in the coil is the same when the magnet is at the top of the coil as when it leaves (I assume necessary symmetry here ).