Question

consider a spherical capacitor composed of two oppositely charged concentric shells separated by a weakly conducting dielectric. the inner shell has a radius of 1.0 cm and holds a charge of -5.0 c while the outer shell has a radius of 9.0 cm and holds a charge of +5.0 c. at time t = 0, charge begins to diffuse from the inner shell into the dielectric, moving outward in a spherically symmetric pattern. what is the direction of the magnetic field at any point in the dielectric between the shells?

the magnetic field points radially inward.
there is no magnetic field between the shells.
the magnetic field points radially outward.
the magnetic field forms concentric circles around the inner shell.

Explanation:

According to Ampère - Maxwell's law, a changing electric field (displacement current) can produce a magnetic field. In this case, as charge diffuses from the inner shell, there is a current (even though it's a displacement current in the dielectric). Using the right - hand rule for the direction of the current (charge moving outward) and the symmetry of the spherical capacitor, the magnetic field forms concentric circles around the central axis (in this case, around the inner shell due to spherical symmetry). Radially inward or outward directions are not correct as magnetic fields around a current (even displacement current) in a symmetric situation (spherical symmetry here, but similar to circular symmetry for the current flow direction) form circular loops. And there is a magnetic field because of the changing electric field (displacement current).

Answer:

The magnetic field forms concentric circles around the inner shell.