Question 178: Electromagnetic Induction

Question

A conducting circular loop is placed in $$X-Y$$ plane in presence of magnetic field $$\overrightarrow{\mathrm{B}}=\left(3 \mathrm{t}^{3} \,\hat{j}+3 \mathrm{t}^{2}\, \hat{k}\right)$$ in SI unit. If the radius of the loop is $$1 \mathrm{~m}$$, the induced emf in the loop, at time, $$\mathrm{t}=2 \mathrm{~s}$$ is $$\mathrm{n} \pi \,\mathrm{V}$$. The value of $$\mathrm{n}$$ is ___________.

Accepted Answer

$${B_ \bot } = 3{t^2}$$
$${{d{B_ \bot }} \over {dt}} = 6t - 12$$ at $$t = 2$$
$${{d{\phi _1}} \over {dt}} = 12 	imes \pi {(1)^2} = 12\pi $$

Electromagnetic Induction

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