A coil of 400 turns of effective area $0.05\, m^2$ is kept perpendicular to a magnetic field of $5 × 10^{-3} T$. When the plane of coil is rotated by 90° around any of its co-planar axis in 0.2 s in magnetic field, the emf induced in the coil is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0.5 V
Given:
$N = 400$
$A = 0.05\,m^2$
$B = 5 \times 10^{-3}\,T$
$\Delta t = 0.2\,s$
Change in magnetic flux:
$\Delta \Phi = B A (\cos 0^\circ - \cos 90^\circ)$
$\Delta \Phi = B A (1 - 0)$
$\Delta \Phi = B A$
Induced emf:
$e = \frac{N \Delta \Phi}{\Delta t}$
$e = \frac{400 \times 5 \times 10^{-3} \times 0.05}{0.2}$
$e = \frac{400 \times 2.5 \times 10^{-4}}{0.2}$
$e = \frac{0.1}{0.2}$
$e = 0.5\,V$
Final Answer: Induced emf = 0.5 V