9. A conducting circular loop is placed in a uniform magnetic field $0.04 T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2 mm/s$. The induced emf in the loop when the radius is $2 cm$ is: (2009)

$4.8\pi \mu V$

$0.8\pi \mu V$

$1.6\pi \mu V$

$3.2\pi \mu V$

Solution:

Induced emf $e = |\frac{d}{dt}(B \pi r^2)| = B \pi \cdot 2r |\frac{dr}{dt}|$.
Substitute $B = 0.04 T$, $r = 0.02 m$, and $|\frac{dr}{dt}| = 2 \times 10^{-3} m/s$.
$e = 0.04 \times \pi \times 2(0.02) \times 2 \times 10^{-3} = 3.2\pi \times 10^{-6} V = 3.2\pi \mu V$.

Rankers Physics

9. A conducting circular loop is placed in a uniform magnetic field $0.04 T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2 mm/s$. The induced emf in the loop when the radius is $2 cm$ is: (2009)

Solution:

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