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

The magnetic field between the plates of a capacitor where $r>R$ is given by (where $r$ is the distance from the axis of plates and $R$ is the radius of each plate of capacitor) (a) $\frac{\mu_{0} i_{b}}{2 \pi R^{2}}$ (b) $\frac{\mu_{0} f_{D}}{2 \pi R}$ (c) $\frac{\mu_{0} i_{0}}{2 \pi r}$ (d) zero

The magnetic field between the plates of a capacitor where $r>R$ is given by (where $r$ is the distance from the axis of plates and $R$ is the radius of each plate of capacitor)
(a) $\frac{\mu_{0} i_{b}}{2 \pi R^{2}}$
(b) $\frac{\mu_{0} f_{D}}{2 \pi R}$
(c) $\frac{\mu_{0} i_{0}}{2 \pi r}$
(d) zero

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Key Concepts

Ampère?Maxwell Law

This law extends Ampère's circuital law by including the displacement current term, allowing one to correctly calculate the magnetic field in regions where there may be a changing electric field but no conduction current. It is crucial for understanding electromagnetic fields in capacitors during charging or discharging.

Displacement Current

Displacement current is an effective current proportional to the rate of change of the electric flux. Introduced by Maxwell, it accounts for the generation of magnetic fields in regions, such as between capacitor plates, where no physical charge flow occurs, ensuring the continuity of current in the equations.

Symmetry in Electromagnetic Field Calculations

In problems involving capacitors or other symmetric configurations, selecting an appropriate Amperian loop exploits the symmetry of the system. This facilitates the integration of the magnetic field around the loop, leading to simplified expressions for the magnetic field outside or inside regions defined by the geometry.

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