Question

A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its palates is increasing at a constant rate with time. The magnetic field arising due to displacement current is ______.

Options

• zero at all places.

• constant between the plates and zero outside the plates.

• non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates.

• zero between the plates and non-zero outside.

Answer 1

A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its palates 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.

Explanation:

Displacement Current,

`I_d = ε_0(dΦE)/(dt)`

= `ε_0(d)/(dt)(EA cos0°)`

= `ε_0A(dE)/(dt)`

= `ε_0A(d)/(dt)((σ)/(ε_0))`

= `A(dσ)/(dt)`

= Constant

Considering the imaginary cylinder connecting the two circular plates of the capacitor, for r < R,

B = `(μ_0I_dr)/(2piR^2)`

r ≥ R

B = `(μ_0I_d)/(2pir)`

Where r = R

B_mx = `(μ_0I)/(2piR)`