Question

A conducting circular loop is placed in a uniform magnetic field of induction $B$ tesla with its plane normal to the field. Now, radius of the loop starts shrinking at the rate $(d r / d t)$. Then the induced e.m.f at the instant when the radius is $r$, is

• A. $\pi r B\left(\frac{d r}{d t}\right)$
• B. $2 \pi r B\left(\frac{d r}{d t}\right)$
• C. $\pi r^{2} B\left(\frac{d r}{d t}\right)$
• D. $\frac{\pi B r^{2}}{2}\left(\frac{d r}{d t}\right)$

Answer 1

Answer: (B)

If the radius is $r$ at a time $t$, then the instantaneous magnetic flux $\phi$ is given by $\phi=\pi r^{2} B$
Now, induced e.m.f. $e$ is given by
$e^{=}-\frac{d \phi}{d t}=-\frac{d}{d t}\left(\pi r^{2} B\right)$
$=-\pi B\left(2 r \frac{d r}{d t}\right)=-2 \pi r B\left(\frac{d r}{d t}\right)$