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) Non-zero everywhere with maximum at the imaginary cylindrical surface connecting peripheries of the plates (b) Zero between the plates and non-zero outside (c) Zero at all places (d) Constant between the plates and zero outside the plates

Answer: (a). Constant dσ/dt gives a constant displacement current Id = ε₀ (dΦE)/(dt). Inside the plates ( r R): B = (μ₀ Id)/(2π r), falling with r. So B is non-zero (except on the axis) and largest at r = R, the cylinder joining the plate edges: answer (a).

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Other: Induction & Displacement Current

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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Answer: (a)

Constant $d\sigma/dt$ gives a constant displacement current $I_d = \varepsilon_0 \frac{d\Phi_E}{dt}$ .
Inside the plates ( $r < R$ ): $B = \frac{\mu_0 I_d r}{2\pi R^2}$ , rising with $r$ .
Outside ( $r > R$ ): $B = \frac{\mu_0 I_d}{2\pi r}$ , falling with $r$ .
So $B$ is non-zero (except on the axis) and largest at $r = R$ , the cylinder joining the plate edges: answer (a).

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