Physics

Problem

A coil of

N

turns and area

A

is rotated with a constant angular speed

\omega

in a uniform magnetic field

B

. At

t=0

the angle between the normal to the coil and the field is

\theta_{0}

(where

0<\theta_{0}<\pi/2

). (i) Show that the instantaneous emf developed in the coil can be written in the form

\mathcal{E}(t)=\mathcal{E}_{0}\sin(\omega t+\phi)

and obtain expressions for

\mathcal{E}_{0}

and the phase angle

\phi

in terms of

B,\,A,\,N,\,\omega

and

\theta_{0}

. (ii) Hence obtain an expression for the rms value of the emf over one complete revolution. (iii) For

N=400

A=3.2\times10^{-2}\,\text{m}^{2}

B=0.20\,\text{T}

\omega=120\,\text{rad\,s}^{-1}

and

\theta_{0}=30^{\circ}

, calculate the rms emf. a. (i) b. (ii) c. (iii)