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 ___________.
Answer (integer)
12
Solution
<p>${B_ \bot } = 3{t^2}$</p>
<p>${{d{B_ \bot }} \over {dt}} = 6t - 12$ at $t = 2$</p>
<p>${{d{\phi _1}} \over {dt}} = 12 \times \pi {(1)^2} = 12\pi$</p>
About this question
Subject: Physics · Chapter: Electromagnetic Induction · Topic: Faraday's Laws
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