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# Electromagnetic induction summary

## Electromagnetic induction summary

The induced e.m.f. $\mathcal{E}$ in a coil of $N$ turns is given by: $$\mathcal{E}=\frac{\Delta(NBA)}{t}$$$\Delta(NBA)$ is the change in magnetic flux linkage (which depends on the number of turns $N$, the magnetic flux density $B$ and the area of the coil $A$).

The induced e.m.f. $\mathcal{E}$ in a straight conductor of length $\ell$ moving perpendicularly to the magnetic field with a speed $v=d/t$ is given by:$$\mathcal{E}= \frac{BA}{t}=\frac{B\ell d}{t}=B\ell v$$

The total charge $Q$ induced in a circuit of resistance $R$ is given by: $$Q=\frac{\Delta\Phi}{R}$$$\Delta\Phi$ is the change in magnetic flux.

Magnetic flux through an area: $\phi=BA$

Magnetic flux linkage through a coil of $N$ turns: $\Phi=N\phi=NBA$

$$\mathcal{E}=-\frac{d\phi}{dt}$$