# Summarizing Electric Generators

## Summary

• An electric generator rotates a coil in a magnetic field, inducing an emfgiven as a function of time by

$$\text{emf}=\text{NAB}\omega \phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\mathrm{\omega t}\text{,}$$

where $$A$$ is the area of an $$N$$-turn coil rotated at a constant angular velocity $$\omega$$ in a uniform magnetic field $$B$$.

• The peak emf $${\text{emf}}_{0}$$ of a generator is

$${\text{emf}}_{0}=\text{NAB}\omega \text{.}$$

## Glossary

### electric generator

a device for converting mechanical work into electric energy; it induces an emf by rotating a coil in a magnetic field

### emf induced in a generator coil

$$\text{emf}=\text{NAB}\omega \phantom{\rule{0.25em}{0ex}}\text{sin}\phantom{\rule{0.25em}{0ex}}\mathrm{\omega t}$$, where $$A$$ is the area of an $$N$$-turn coil rotated at a constant angular velocity $$\omega$$ in a uniform magnetic field $$B$$, over a period of time $$t$$

### peak emf

$${\text{emf}}_{0}=\text{NAB}\omega$$