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  4. A semicircular wire of radius R is rotated with constant angular velocity about an axis passing through one end and perpendicular to the plane of the wire. There is a uniform magnetic field of strength B. The induced emf between the ends is

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Q. A semicircular wire of radius $R$ is rotated with constant angular velocity about an axis passing through one end and perpendicular to the plane of the wire. There is a uniform magnetic field of strength $B$. The induced emf between the ends isPhysics Question Image

Electromagnetic Induction

Solution:

We connect a conducting wire from $A$ to $C$ and complete the semicircular loop.
The emf in the semicircular loop is zero because its magnetic flux does not change.
$\therefore$ emf of section $A P C+$ emf of section $C Q A=0$
$\therefore $ emf of section $A P C=$ emf of section $A Q C=2 B R^{2} \omega$

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