A parallel-plate capacitor with circular plates of radius 0.10 m is being discharged. A circula

step 1 This problem covers the concept of the drift current and first we need to find the enclosed elec

A parallel-plate capacitor with circular plates of radius...

A parallel-plate capacitor with circular plates of radius $0.10 \mathrm{~m}$ is being discharged. A circular loop of radius $0.20 \mathrm{~m}$ is concentric with the capacitor and halfway between the plates. The displacement current through the loop is 2.0 A. At what rate is the electric field between the plates changing?

Key Concepts

Rate of Change of the Electric Field

The rate of change of the electric field in a region is directly related to the displacement current through that region. When the electric field changes in time, the resulting change in electric flux gives rise to a displacement current. By knowing the displacement current and the area over which the electric field is present, one can determine the rate at which the electric field is changing.

Effective Integration Area

When applying the concept of displacement current, it is important to choose an appropriate integration surface that captures the region where the electric field is nonzero. In the case of a capacitor, although a loop might be larger than the plates, only the area of the plates carries the electric field, and this restricted area is used to compute the total electric flux variation.

Displacement Current

Displacement current is the effective current term that arises from a time-varying electric field, introduced by Maxwell to modify Ampère’s law. It accounts for the changing electric flux in regions where no conduction current exists, ensuring that the continuity of current is maintained even in situations, such as within a capacitor, where charges are not physically moving through the gap.

Maxwell–Ampère Law

The Maxwell–Ampère law is an extension of Ampère’s law that incorporates the displacement current. It states that the line integral of the magnetic field around a closed path is proportional to the sum of the conduction current and the displacement current through any surface bounded by that path. This law is crucial when dealing with time-varying fields in systems like capacitors.

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