Question

A circular coil of radius $8.0$ $cm$ and $20$ turns rotates about its vertical diameter with an angular speed of $50$ $m/s^{-1}$ in a uniform horizontal magnetic field of magnitude $3\times {10}^{-2}$ $T$. Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance $10$ $\Omega$. How much power is dissipated as heat?

Answer 1

$r=8$ $cm=8\times {10}^{-2}$ $m$

$A=\pi r^2=64\times {10}^{-4}\times \pi$ $m^2$

$N=20$

$\omega =50$ $rad{s}^1$

Concept: $\varphi =B\cdot A$

$\Rightarrow \varphi =B\pi r^2\cos \theta$

$ϵ=-N\frac{d\varphi }{dt}$

$\Rightarrow |ϵ|=NB\pi r^2\omega \sin \omega t$

${ϵ}_o=NBA\omega$

$\Rightarrow {ϵ}_o=20\times 3\times {10}^{-2}\times 64\times {10}^{-4}\times \pi \times 50$

Max. ${ϵ}_o=0.603$ $volt$

Average EMF over a cycle $=0$ $V$

$I_o=\frac{{ϵ}_o}{R}=\frac{0.603}{10}=0.0603$ $A$

Power loss $=\frac{1}{2}{E}_o{I}_o=\frac{1}{2}\times 0.0603\times 0.603=0.018$ $W$