Question

A circular coil of mean radius of 7 cm and having 4000 tums is rotated at the rate of 1800 revolutions per minute in the earth's magnetic field (B = 0.5 Gauss ) , The peak value of emf induced is

• A. 1 . 158 V
• B. 0 . 58 V
• C. 0 . 29 V
• D. 5 . 8 V

Answer 1

The correct option is B 0 . 58 V

Given,

Angular frequency $\omega =2\pi f=\frac{2\pi 1800}{60}=60\pi$

Magnetic field, $B=0.5G=0.5\times {10}^{-4}T$

Area, $A=\pi \times {0.07}^2=0.0154m^2$

Flux $\varphi =nBA\cos \theta =nB\left(\pi r^2\right)\cos \omega t$

The induced emf is

$\epsilon =\frac{-d\varphi }{dt}=nBA\omega \sin \omega t$

For maximum E.M.F, $\epsilon ={\epsilon }_o,\sin \omega t=1$

${\epsilon }_o=n\omega BA$

${\epsilon }_o=4000\times 60\pi \times 0.5\times {10}^{-4}\times 0.0154$

${\epsilon }_o=0.58V$