Question

A circular coil of radius $8cm$, $400$ turns and resistance $2Omega$ is placed with its plane perpendicular to the horizontal component of the earths magnetic field. It is rotated about its vertical diameter through $180^{\circ }$ in $0.30s$. Horizontal component of earth magnetic field at the place is $3\times 10^{-5}T$ The magnitude of current induced in the coil is approximately

• A. $4\times 10^{-2}A$
• B. $8\times 10^{-4}A$
• C. $8\times 10^{-2}A$
• D. $1.92\times 10^{-3}A$

Answer 1

Answer: (B)

Initial flux through the coil
${\varphi }_i=BAcos\theta$
$=3\times 10^{-5}\times \pi \times (8\times 10^{-2}{)}^2\times cos{0}^{\circ }$
$=192\pi \times 10^{-9}WB$
Final flux after the rotation
${\varphi }_f=3\times 10^{-5}\times \pi \times (8\times 10^{-2}{)}^2\times cos180^{\circ }$
$=-192\pi \times 10^{-9}Wb$
$\therefore$ The magnitude of induced emf is
$\epsilon =N\frac{|d\varphi |}{dt}=\frac{N|{\varphi }_f-{\varphi }_i|}{dt}$
$=\frac{400\times \left(384\pi \times 10^{-9}\right)}{0.30}$
$=1.6\times 10^{-3}V$
Current, $I=\frac{\epsilon }{R}$
$=\frac{1.6\times 10^{-3}}{2}$
$=8\times 10^{-4}A$