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:

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  1. zero at all places
  2. constant between the plates and zero outside the plates
  3. non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates
  4. zero between the plates and non-zero outside

Answer (Detailed Solution Below)

Option 3 : non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates
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Detailed Solution

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Correct option is : (3) Non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates

Let the surface charge density be σ = q / A

Given dq/dt = constant

⇒ d/dt (q / A) = constant ⇒ (1 / A) × dq/dt = constant

It means displacement current is constant.

This system will act like a cylindrical wire.

The graph of magnetic field (B) vs radius (r) is:

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