Topology of Mangetic Field within Two Plate Tubular Capacitor

I refer to two conductive tubes, one slightly smaller in diameter, slid axially into each other with dielectric film between their opposing surfaces.

If I apply an AC voltage from a transformer across the two tubes to create a radial, alternating electric potential, what does the shape (vectoral orientation) of the accompanying magnetic field look like in the following two instances?

1. Both tubes are of the same length.

2. The outer tube is twice the length of the inner tube which is centered lengthwise.

Is this school/college Homework?

Let me guess then. The B field is at right angle to the E field, extending out the ends of the tubes.

Now what happens to that B field if a convex (facing inward) metal cap is added to both ends of the outer tube so that the same charge that is applied to the outer tube sits on its interior surface? Would this cancel the B field, similar to what occurs in a charged spherical cap?