# Math Help - Electromagnetic induction

1. ## Electromagnetic induction

Can anyone help me derive an expression for the e.m.f induced in a coil rotating in a uniform magnetic field.

let
w= angular velocity etc..........

2. When the coil is rotated at a uniform rate in a uniform horizontal magnetic field of intensity $\vec{B}$, then the induced e.m.f produced is given by:

$e = -\frac{d\phi}{dt}$

$= -\frac{d}{dt}[N\vec{B}\cdot \hat{n} A]$

Where N = number of turns in coil

and A = Area of coil

$= -\frac{d}{dt}[NBcos{\theta}A]$

$= -NAB\frac{d}{dt}[cos{\theta}]$

$= -NAB\left[-sin{\theta}\frac{d\theta}{dt}\right]$

$= NAB\omega sin{\omega t}$

Where $\omega = \frac{d\theta}{dt} = \frac{\theta}{t}, \text{as it is uniform}$

$\therefore \ e = (NAB\omega)sin(\omega t)$

$e = e_0 \ sin{(\omega t)}$

And there you go.