Question

A coil of 1200 turns and mean area of $500c{m}^2$ is held perpendicular to a uniform magnetic field of induction $4\times {10}^{-4}.$ The resistance of the coil is 20 $\Omega$ . When the coil is rotated through $180{}^{\circ }$ in the magnetic field in 0.1 s the average electric current (in mA) induced is :

• A. 12
• B. 24
• C. 36
• D. 48

Answer 1

Answer: (B)

In perpendicular position in uniform magnetic field, magnetic field linked with the each turn of coil $\text{o}{|}_1=BA$ On rotating coil through ${180}^o,$ flux linked $\text{o}{|}_2=-BA$ $\therefore$ Change in magnetic flux $\Delta \text{o }|=\text{o}{|}_2-\text{o}{|}_1=-2BA.$ $\therefore$ emf induced in the coil $e=-N\frac{\Delta \text{o }|}{\Delta t}$ $=\frac{2NBA}{\Delta f}$ where N is the number of turns in the coil. The current in the coil $i=\frac{e}{R}=\frac{2NBA}{R\Delta \mathrm{T}}$ $=\frac{2\times 1200\times 4\times {10}^{-4}\times 500\times {10}^{-4}}{20\times 0.1}$ $=2400\times {10}^{-5}$ $=24\times {10}^{-3}A$ $=24mA$