NEET 2025 — Physics solution

NEET2025Physics

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:

A
zero at all places
B
constant between the plates and zero outside the plates
C
non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates
D
zero between the plates and non-zero outside

Solution

Displacement current density: $I_{d} = ϵ_{0} \frac{d ϕ _{E}}{d t} = ϵ_{0} A \frac{d E}{d t}$ . Since $E = σ / ϵ_{0}$ , we get $I_{d} = A \frac{d σ}{d t}$ , which is constant in time and uniformly distributed across the area between the plates.

Applying Ampere–Maxwell law on circular loops of radius $r$ between the plates: for $r < R$ (plate radius), the enclosed displacement current grows as $r^2$, giving $B\propto r$. For $r > R $, t h ee n c l ose dd i s pl a ce m e n t c u r r e n t i sco n s t an t, g i v in g$ B\propto 1/r$.

So $B$ is non-zero both inside and outside the imaginary cylinder, peaking exactly at $r = R$ — the cylindrical surface connecting the plate edges.

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