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  4. A conducting circular loop of radius (10/√π) cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is:

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Q. A conducting circular loop of radius $\frac{10}{\sqrt{\pi}} cm$ is placed perpendicular to a uniform magnetic field of $0.5 T$. The magnetic field is decreased to zero in $0.5 s$ at a steady rate. The induced emf in the circular loop at $0.25 s$ is:

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Solution:

$ EMF =\frac{ d \phi}{ dt }=\frac{ BA -0}{ t } $
$ A =\pi r ^2=\pi\left(\frac{0.1^2}{\pi}\right)=0.01$
$ B =0.5 $
$ EMF =\frac{(0.5)(0.01)}{0.5}=0.01 \,V =10 \,mV $