Question

A circular coil of mean radius of $7\, cm$ and having $4000$ turns is rotated at the rate of $1800$ revolutions per minute in the earth's magnetic field $(B=0.5$ gauss), the emf induced in coil will be

• A. 1.158 V
• B. 0.58 V
• C. 0.29 V
• D. 5.8 V

Answer 1

The Correct Option is B

Here: $n=4000,\, B=0.5 \times 10^{-4} Wb / m ^{2}$
Rate of rotation of coil $=1800\, rev / \min$
$=\frac{1800}{60}=30\, rev / \sec$
$\omega=2 \pi f=2 \pi \times 30=60\, \pi\, rad / s$
$r=7\, cm =0.07\, m$
Now area of coil
$A=\pi r^{2}=\pi \times(0.07)^{2}=49\, \pi \times 10^{-4} m ^{2}$
Now the maximum energy induced is
$e =B A n \omega$
$=0.5 \times 10^{-4} \times 49\, \pi \times 10^{-4} \times 4000 \times 60\, \pi$
$=0.58\, V$