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Q.

A metalic rod of length ‘L’ is rotated with an angular speed of $‘ ω ’$ normal to a uniform magnetic field ‘B’ about an axis passing through one end of rod as shown in figure. The induced emf will be:

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a

$\frac{1}{4} B^{2} L ω$

b

$\frac{1}{2} B L^{2} ω$

c

$\frac{1}{4} B L^{2} ω$

d

$\frac{1}{2} B^{2} L^{2} ω$

answer is C.

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Detailed Solution

Question Image
$\int d ε = \int B (ω x) d x$
$ε = B ω \int_{0}^{L} x d x = \frac{B ω L^{2}}{2}$

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A metalic rod of length ‘L’ is rotated with an angular speed of ‘ω’ normal to a uniform magnetic field ‘B’ about an axis passing through one end of rod as shown in figure. The induced emf will be: