Question

If the radius of a coil is changing at the rate $10^{-2}$ units in a normal magnetic field $10^{-3}$ units, the induced emf is $1\mu V$. What is the final radius of the coil?

• A. 1.6cm
• B. 16cm
• C. 12cm
• D. 1.2cm

Answer 1

Answer: (A)

Induced emf is given by
$|e|=\frac{d\varphi }{dt}=B\frac{dA}{dt}$
$(\because \varphi =BA)$
$=\pi B\frac{d}{dt}\left(r^2\right)=\pi B.2r\frac{dr}{dt}$
Given, $\frac{dr}{dt}=10^{-2}$ units,
$B=10^{-3}$ units, $e=1\mu V$
$\therefore 1\times 10^{-6}=3.14\times 10^{-3}\times 2\times r\times 10^{-2}$
or $r=\frac{10^{-6}}{3.14\times 10^{-5}\times 2}$
$=0.016m=1.6cm$