Question

A long thin wooden cylindrical pipe of radius R, carrying a uniform surface charge density $\sigma$, is rotating about its axis with an angular velocity $\omega$ that increases slowly with time as $\omega =kt$, $k$ is constant. Which of the statements are correct for region inside the pipe?

• A. Magnetic field is uniform and constant with time.
• B. Magnetic field is not constant with time.
• C. Electric field is zero.
• D. Electric field is not zero.

Answer 1

Answer: (B), (D)

Electric field is not zero.

The rotating wodden cylinder behaves like a solenoid. The magnetic field inside a solenoid is proportional to current; similarly, the magnetic field inside the rotating cylinder is proportional to its angular speed. Thefore the magnetic field inside is chaging with time. As the magnetic field is changing with time, from Faraday's law, there will be an induced electric field.