A metallic rod of length is rotated with an angular speed normal to a uniform magnetic field about an axis passing through one end of the rod as shown in the figure. The induced emf will be [2023]

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Solution

Q.
A metallic 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 the rod as shown in the figure. The induced emf will be [2023]

1 $\frac{1}{2} B^{2} L^{2} ω$

2 $\frac{1}{4} B L^{2} ω$

3 $\frac{1}{2} B L^{2} ω$

4 $\frac{1}{4} B^{2} L ω$

Ans.
(3)

$\int d ε = \int B (ω x) d x$

$ε = B ω \int_{0}^{L} x d x = \frac{B ω L^{2}}{2}$

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