A cylindrical region contains a uniform electric field that is along the cylinder axis and is changing with time. If r is distance from the cylinder axis the magnitude of the magnetic field within the region is:

This MCQ is related to the magnetic field inside a cylindrical region that contains a uniform electric field which is changing with time.

When an electric field is changing with time, it produces a magnetic field. This phenomenon is known as electromagnetic induction, which is described by Faraday’s law of induction.

In this case, the electric field is uniform and is along the cylinder axis. Therefore, the magnetic field produced by the changing electric field will also be along the cylinder axis.

Now, the magnitude of the magnetic field inside the region depends on the distance from the cylinder axis, denoted by r. The answer choices give different possible variations of the magnetic field with respect to r.

Option E, “proportional to r”, is the correct choice.

This is because the magnetic field produced by the changing electric field is directly proportional to the distance from the cylinder axis. As r increases, the magnetic field also increases proportionally. Therefore, the magnetic field is not uniform but varies with r, and it is not proportional to 1/r or r^2 or 1/r^2, which are incorrect choices.