First slide

Faraday's law of Electromagnetic induction

Question

A metallic ring of radius 1 m is placed in a uniform magnetic field of induction $1 μ T$ with its plane perpendicular to the direction of magnetic field. Now the radius of the ring is halved in a time interval of 0.1 second. Then average emf induced in the ring is

Moderate

A

$7.5 μ V$
B

$12 π μ V$
C

$25 π μ V$
D

$15.5 π μ V$

Solution

$\begin{array}{l} A v e r a g e e m f = \frac{B . π r^{2} - B . π {(r / 2)}^{2}}{Δ t} \\ = \frac{3}{4} π r^{2} . \frac{B}{Δ t} = \frac{3}{4} π {(1)}^{2} . \frac{1}{0.1} μ V \\ = 7.5 π μ . V \end{array}$

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