A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is:
- Non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates
- Zero between the plates and non-zero outside
- Zero at all places
- Constant between the plates and zero outside the plates
Answer
(1) Non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates
Solution
increases at a constant rate, so E = 0 changes at a constant rate and the displacement current Id = 0 d Edt is constant and uniform over the plate area.
Ampere–Maxwell law for a circle of radius r (plate radius R):
Inside (r < R): B 2 r = 0 Id r2R2 B = 0 Id r2 R2 (increases with r).
Outside (r > R): B = 0 Id2 r (decreases with r).
So B is non-zero everywhere (except on the axis) and is maximum at r = R, the cylindrical surface joining the peripheries of the plates.
Answer: (1)