Question

A metallic stick of length \( L \) confined in a plane is rotated in its own plane with angular velocity \( \omega \) in a uniform magnetic field \( \vec{B} \) exists in the region. Find the expression of emf induced between the ends of the stick.

Hint:

When a conductor moves in a magnetic field, the induced emf depends on the speed of the conductor, its length, and the magnetic field strength.

Answer 1

Step 1: Understanding the setup.
When a metallic stick is rotated in a magnetic field, the emf induced between the ends of the stick is due to the motion of the conductive material in the magnetic field. The induced emf is given by: \[ \mathcal{E} = B \omega L^2 \] where: - \( B \) is the magnetic field strength, - \( \omega \) is the angular velocity, - \( L \) is the length of the stick.
Step 2: Conclusion.
The induced emf between the ends of the stick is: \[ \mathcal{E} = B \omega L^2 \]