Question

A conducting circular loop is placed in a uniform magnetic field, $B = 0.025\, T$ with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of $1 \,mm \,s^{-1}$. The induced emf when the radius is $2 \,cm$, is

• A. $2\pi \, \mu V$
• B. $\pi \,\mu V$
• C. $\frac{\pi}{2}\,\mu V$
• D. $2\, \mu V$

Answer 1

Answer: (B)

$\pi \,\mu V$

Answer 2

Here, Magnetic field, $B=0.025\,T$ Radius of the loop, $r=2\, cm=2\times10^{-2}\, m$ Constant rate at which radius of the loop shrinks, $\frac{d r}{d t}=1\times10^{-3}\,m\,s^{-1}$ Magnetic flux linked with the loop is $\phi=BA\, cos\theta =B \left(\pi r^{2}\right)cos0^{\circ}=B\pi r^{2}$ The magnitude of the induced emf is $\left|\varepsilon\right|=\frac{d \phi}{d t}=\frac{d}{d t}\left(B\pi r^{2}\right)=B\pi2r \frac{dr}{d t}$ $=0.025\times\pi\times2\times2\times10^{-2}\times1\times10^{-3}$ $=\pi\times10^{-6}\, V =\pi\,\mu V$