Question

A circular coil of radius $10\, cm , 500$ turns and resistance $2 \Omega$ is placed with its plane perpendicular to the horizontal component of the earth's magnetic field. It is rotated about its vertical diameter through $180^{\circ}$ in 0.25 s (Horizontal component of the earth's magnetic field at place is $3.0 \times 10^{-5} T$ ). Estimate the induced current in the coil.

• A. $1.2 \times 10^{-3} A$
• B. $1.9 \times 10^{-3} A$
• C. $2.3 \times 10^{-3} A$
• D. $2.8 \times 10^{-3} A$

Answer 1

Answer: (B)

$\phi_{B \text { (initial) }} =B A \cos \theta=\left(3 \times 10^{-5}\right)\left(\pi \times 10^{-2}\right) \cos 0^{\circ}$
$=3 \pi \times 10^{-7} Wb$
flux after rotation,
$\phi_{B(\text { final })}=\left(3 \times 10^{-5}\right)\left(\pi \times 10^{-2}\right) \cos 180^{\circ}$
$=-3 \pi \times 10^{-7} Wb$
Estimated value $\varepsilon=N\left|\frac{\Delta \phi}{\Delta t}\right|$
$=\frac{500 \times 6 \pi \times 10^{-7}}{0.25}$
$=3.8 \times 10^{-3} V$
$I=\frac{\varepsilon}{R}$
$=\frac{3.8 \times 10^{-3}}{2}$
$=1.9 \times 10^{-3} A$