The magnetic field between the plates of a capacitor when...

The magnetic field between the plates of a capacitor when $r>R$ is given by
(A) $\frac{\mu_{0} I_{D} r}{2 \pi R^{2}}$
(B) $\frac{\mu_{0} I_{D}}{2 \pi R}$
(C) $\frac{\mu_{0} I_{D}}{2 \pi r}$
(D) $\mathrm{kWU}$

Key Concepts

Ampère's Law

Ampère's Law states that the line integral of the magnetic field around any closed loop is proportional to the total current passing through the loop. In the context of capacitors, this law is modified by Maxwell to include the effect of a changing electric field, leading to the displacement current term.

Maxwell’s Displacement Current

Maxwell introduced the concept of displacement current to account for the magnetic field produced by a time-varying electric field, particularly in regions where there is no physical current, such as between the plates of a charging capacitor. This term is crucial for maintaining the continuity of current in Ampère’s law.

Electromagnetic Fields in Capacitors

Between the plates of a capacitor, a time varying electric field exists, which gives rise to a displacement current. This displacement current produces a magnetic field similar to that produced by a conduction current in a wire, allowing the use of Ampère-Maxwell's law to compute the magnetic field in the region between the plates.

Symmetry in Field Calculations

Many electromagnetic problems, including the calculation of magnetic fields around capacitors, benefit from exploiting symmetry. When the configuration exhibits circular symmetry, it simplifies the application of Ampère's law, leading to formulas where the magnetic field depends inversely on the radial distance from the central axis, as seen in the correct expression.

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