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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:

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

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.