JEE Main & Advanced Sample Paper JEE Main Sample Paper-47

  • question_answer
    An equilateral triangular loop having a resistance R and length of each side\[l\]is placed in a magnetic field which is varying at \[\frac{dB}{dt}=1T/s\]. The induced current in the loop will be

    A)  \[\frac{\sqrt{3}}{4}\frac{{{l}^{2}}}{R}\]

    B)  \[\frac{4}{\sqrt{3}}\frac{{{l}^{2}}}{R}\]

    C)  \[\frac{\sqrt{3}}{4}\frac{R}{{{l}^{2}}}\]            

    D)  \[\frac{4}{\sqrt{3}}\frac{R}{{{l}^{2}}}\]

    Correct Answer: A

    Solution :

                 With the help of information?s in the equation. \[\phi =\frac{\sqrt{3}}{4}{{I}^{2}}B,\,\,\Rightarrow \,\,\varepsilon =\left| \frac{d\phi }{dt} \right|=\frac{\sqrt{3}}{4}{{I}^{2}}\,\frac{dB}{dt},\] \[\therefore \]    \[I=\frac{\pi }{R}=\,\frac{\sqrt{3}{{I}^{2}}}{4R}\]

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