Question 14

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

The linear speed of this small element is given by $$v = r\omega$$.

The motional EMF induced in this small element $$dr$$ is $$d\epsilon = B v \, dr = B(r\omega) \, dr$$.

$$\epsilon = \int_{0}^{L} B\omega r \, dr$$

$$\epsilon = \frac{1}{2} B\omega L^2$$

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