Question

a cylindrical capacitor is being charged by an exponentially decreasing current. the inner cylinder of the capacitor is positive and the outer cylinder is negative. what is the direction of the magnetic field between the two cylinders while the capacitor is charging?
the magnetic field is concentric with the cylinders.
the magnetic field points radially from the inner cylinder to the outer cylinder.
the magnetic field points radially from the outer cylinder to the inner cylinder.
there is no magnetic field between the cylinders.

Explanation:

When a capacitor is charging, there is a displacement current. For a cylindrical capacitor, using Ampère - Maxwell's law, the symmetry of the problem (cylindrical geometry) implies that the magnetic field lines form concentric circles around the axis of the cylinders. Radial magnetic fields would violate the symmetry and the nature of magnetic field generation (magnetic field lines are closed loops). Also, since there is a (displacement) current during charging, there is a non - zero magnetic field.

Answer:

The magnetic field is concentric with the cylinders.