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Physics Question 26 – NEET-UG 2025

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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 :

Recall that a changing electric field gives rise to a displacement current, which acts as a source of magnetic field.

Step 1: Understand Displacement Current and Magnetic Field Generation✦ Active

When a parallel plate capacitor is being charged, the electric field between its plates changes with time. This changing electric field gives rise to a displacement current (Id=ϵ0dΦEdt) between the plates. According to Ampere-Maxwell's law, this displacement current acts as a source of a magnetic field, similar to a conduction current.

Step 2: Analyze Magnetic Field Distribution○ Expand

For a circular parallel plate capacitor, the displacement current density is uniform between the plates. Using Ampere-Maxwell's law with an Amperian loop of radius r concentric with the plates:

∮B→⋅dl→=μ0Id

1. **Inside the plates (r<R):** The magnetic field B increases linearly with r (B∝r). This means it's non-zero and increases from the center to the edge.

2. **Outside the plates (r>R):** The total displacement current enclosed by the loop is constant (equal to the total displacement current flowing through the capacitor). In this region, B∝1r. This means the magnetic field is non-zero but decreases as r increases.

💡 Teacher's Secret Hint

Remember that the displacement current density is uniform across the area of the plates, but the total displacement current enclosed by an Amperian loop depends on its radius.

Step 3: Determine Maximum Magnetic Field Location○ Expand

From the analysis in Step 2, the magnetic field is non-zero both inside and outside the plates. It increases from the center to the edge of the plates and then decreases outside the plates. Therefore, the magnetic field will be maximum at the periphery of the plates, which is the imaginary cylindrical surface connecting the peripheries of the circular plates.

💡 Teacher's Secret Hint

The magnetic field behaves similarly to that of a long straight wire carrying current, but with the current distributed over the area of the plates for the 'inside' region.

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