# 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: $$\Phi=N\phi=NBA$$

**Faraday's law**:

**Lenz' law**: the magnetic field produced by an induced current opposes the change in magnetic flux that induced that current.

**Fleming's right hand rule**: motion (thumb), field (index), current (middle).

**Right** hand rule is used for **generators**.

**Left** hand rule is used for **motors**.