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A conducting circular loop is placed in \mathrm{X-\mathrm{Y}} plane in presence of magnetic field \mathrm{}\vec{B}=\left(3 t^{3} \hat{j}+3 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__________.

Option: 1

6


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{\bar{B}=3 t^3(\hat{j})+3 t^2(\hat{k})}

\mathrm{r=1 \mathrm{~m}}

\mathrm{e=\left|\frac{d}{d t}(\bar{B} \bar{A})\right|}

\mathrm{\bar{A}=\pi \left ( 1 \right )^{2}\hat{k}}

\mathrm{\Phi =\bar{B} \cdot \bar{A}=3 \pi t^2}

\mathrm{e=\left|\frac{d(\phi)}{d t}\right|=3 \pi(2 t)}

\mathrm{\text { at } t=2 \mathrm{~s} \text {, }}

\mathrm{e=6 \pi V}

The value of n is 6








 

Posted by

vishal kumar

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