What is the relation between the permittivity of free  space ${\epsilon }_0$, the permeability of free space ${\mu }_0$ and the speed of light in a vacuum?

What does the Maxwell's equation explain?

A variable frequency ac source Is connected to a capacitor. How will the displacement current change with decrease in frequency?

A long straight cable of length $l$ is placed symmetrically along $z$-axis and has radius $a\left(<<l\right)$. The cable consists of a thin wire and a co-axial conducting tube. An alternating current $I\left(t\right)=I_0\sin \left(2\pi \nu t\right)$ flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance $\mathrm{s}$ from the wire inside the cable is $E \left(s, t\right)={\mu }_0{I}_0\nu \cos \left(2\pi vt\right)$ In $\left(\frac{\mathrm{s}}{\mathrm{a}}\right)\hat{k}$.

Calculate the displacement current density inside the cable.

A long straight cable of length $l$ is placed symmetrically along $z$-axis and has radius $a\left(<<l\right)$. The cable consists of a thin wire and a co-axial conducting tube. An alternating current $I\left(t\right)=I_0\sin \left(2\pi \nu t\right)$ flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance $\mathrm{s}$ from the wire inside the cable is $E \left(s, t\right)={\mu }_0{I}_0\nu \cos \left(2\pi vt\right)$ In $\left(\frac{\mathrm{s}}{\mathrm{a}}\right)\hat{\mathrm{K}}$.

Compare the conduction current $I_{\mathit{0}}$ with the dispalcement current d $I_o^d$.