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Q.

A wire of length L is bent to form a semicircle. The wire rotates about its one end with angular velocity $ω$ Axis of rotation being perpendicular to plane of the semi circle. In the space a uniform magnetic field B exists as shown. Then potential difference between M and N is

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a

\frac{1}{4} B ω L^{2}

b

\frac{1}{2} B ω L^{2}

c

\frac{2B ω L^{2}}{π^{2}}

d

\frac{B ω L^{2}}{π^{2}}

answer is B.

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Detailed Solution

Question Image

Effective length between M and N is diameter of semicircle i.e.,

$x = 2 r$

$x = 2 (L/ π)$

$E_{MN} = \frac{1}{2} B x^{2} ω$

$= \frac{1}{2} B ω \frac{4 L^{2}}{π^{2}} = \frac{2 B ω L^{2}}{π^{2}}$

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A wire of length L is bent to form a semicircle. The wire rotates about its one end with angular velocityω Axis of rotation being perpendicular to plane of the semi circle. In the space a uniform magnetic field B exists as shown. Then potential difference between M and N is