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(D) Given: Magnetic field $B = 0.4\,T$,rate of change of radius $\frac{dr}{dt} = 1\,mm/s = 10^{-3}\,m/s$,and radius $r = 2\,cm = 2 	imes 10^{-2}\,m$.

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(D) Given: Magnetic field $B = 0.4\,T$,rate of change of radius $\frac{dr}{dt} = 1\,mm/s = 10^{-3}\,m/s$,and radius $r = 2\,cm = 2 	imes 10^{-2}\,m$.The area of the circular loop is $A = \pi r^2$.The rate of change of area is $\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$.According to Faraday's law,the magnitude of induced emf is $\varepsilon = \left| \frac{d\phi}{dt} ight| = \left| \frac{d(BA)}{dt} ight| = B \frac{dA}{dt}$.Substituting the values:$\varepsilon = 0.4 	imes (2 	imes \pi 	imes 2 	imes 10^{-2} 	imes 10^{-3})\,V$$\varepsilon = 0.4 	imes 4\pi 	imes 10^{-5}\,V$$\varepsilon = 1.6\pi 	imes 10^{-5}\,V = 16\pi 	imes 10^{-6}\,V = 16\pi\,\mu V$.Since $16\pi \approx 16 	imes 3.14 = 50.24\,\mu V$,the closest integer value is $50\,\mu V$.

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