A circular coil of diameter 15 mm having 300 turns is placed in a magnetic field of 30 mT such that the plane of the coil is perpendicular to the direction of magnetic field. The magnetic field in reduced uniformly to zero in 20 ms and again increased uniformly to 30 mT in 40 ms . If the emfs induced in the two time intervals are ${e}_{1}$ and ${e}_{2}$ respectively, then the value of ${e}_{1}/{\mathrm{e}}_{2}$ is

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Correct answer: c) 2. Use Faraday's law: $E=NA\frac{\Delta B}{\Delta t}$. Area $A$ and $N$ cancel in the ratio. $\frac{{e}_{1}}{{e}_{2}}=\frac{\Delta B\mathrm{/}\Delta {t}_{1}}{\Delta B\mathrm{/}\Delta {t}_{2}}=\frac{(30\times {10}^{−3})\mathrm{/}(20\times {10}^{−3})}{(30\times {10}^{−3})\mathrm{/}(40\times {10}^{−3})}=\frac{30\mathrm{/}20}{30\mathrm{/}40}=\frac{40}{20}=2.$ So ${e}_{1}\mathrm{/}{e}_{2}=2.$

A circular coil of diameter 15 mm having 300 turns is placed in a magnetic field of 30 mT such that the plane of the coi…

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