What is displacement current, and why did Maxwell introduce it?

The electric flux through a surface changes at \(2.0\times10^{10}\,\mathrm{V\,m\,s^{-1}}\). Find the displacement current in vacuum.

Write the Ampere-Maxwell law in integral form for a loop bounding a surface in vacuum.

A parallel-plate capacitor has plate area \(0.020\,\mathrm{m^2}\). The electric field between the plates increases at \(5.0\times10^6\,\mathrm{V\,m^{-1}\,s^{-1}}\). Find \(I_d\) in air.

A capacitor has \(C=5.0\,\mu\mathrm{F}\) and its voltage changes at \(4.0\times10^3\,\mathrm{V\,s^{-1}}\). Find the displacement current between the plates.

What is the displacement current density in vacuum if \(dE/dt=3.0\times10^7\,\mathrm{V\,m^{-1}\,s^{-1}}\)?

A capacitor is being charged by a \(0.60\,\mathrm{A}\) current in its wires. What is the displacement current in the gap between the plates?

A circular parallel-plate capacitor of radius \(R=0.050\,\mathrm{m}\) is charging with current \(I=2.0\,\mathrm{A}\). Find the magnetic field at radius \(r=0.020\,\mathrm{m}\) between the plates, assuming uniform displacement current density.

A circular capacitor is charging with current \(I=2.0\,\mathrm{A}\). Find the magnetic field at \(r=0.10\,\mathrm{m}\), outside the plate radius.

Why does the original Ampere's law give an apparent contradiction for a charging capacitor?

Does displacement current mean that charges physically cross the empty space between capacitor plates?

Check the units of \(\epsilon_0 d\Phi_E/dt\). What physical unit should it have?

A dielectric with \(\kappa=4.0\) fills a capacitor. If \(A=0.010\,\mathrm{m^2}\) and \(dE/dt=2.0\times10^6\,\mathrm{V\,m^{-1}\,s^{-1}}\), find \(I_d\) using \(\epsilon=\kappa\epsilon_0\).

For a steady electric field between capacitor plates, what is the displacement current?

The field between capacitor plates is \(E(t)=E_0\sin\omega t\). Write the displacement current for plate area \(A\) in vacuum.

Why is displacement current important in electromagnetic waves?

A charging current increases the electric flux between plates linearly from \(0\) to \(6.0\times10^9\,\mathrm{V\,m}\) in \(0.30\,\mathrm{s}\). Find \(I_d\).

A loop encloses no conduction current, but the electric flux through its surface is changing. Can \(\oint \vec B\cdot d\vec l\) be nonzero?

Explain why displacement current is not optional in a time-varying circuit model.

A capacitor has plate radius \(0.040\,\mathrm{m}\) and is charging with \(I=0.50\,\mathrm{A}\). What fraction of the displacement current is enclosed by an Amperian circle of radius \(0.020\,\mathrm{m}\) between the plates?