Question

A cylindrical parallel-plate capacitor is charged with a time varying current I(t) = dQ/dt. How does the magnetic field in the capacitor vary with distance from the central axis of the capacitor while still inside the capacitor?

(a) The magnetic field is constant and zero.
(b) The magnetic field is constant and non-zero.
(c) The magnetic field increases in strength as you move away from the center.
(d) The magnetic field decreases in strength as you move away from the center.
(e) Toby

Answer 1

Answer is option c and the answer lies in applying Ampere's law.

(c) The magnetic field increases in strength as you move away from the center.

According to Ampere's law the magnetic field is proportional to the current enclosed in the Amperian loop. The current is distributed throught out the capacitor. Therefore, if we calculate the magnetic field at a point near the centre, we are only enclosing a small fraction of the total current. As we move away from the centre, we start enclosing the entire current that is distributed throughout the whole capacitor.

Therefore, The magnetic field increases in strength as you move away from the center.