Question

Show that the dimensions of the displacement current ε0dφEdt are that of an electric current.

Answer 1

Both are quantities of Maxwell's Equations

Explanation:

• Electromagnetism describes that displacement current can be called as a quantity that appears in Maxwell's equations which can be defined in terms of rate of change of electric displacement field.

• Displacement current & electric current density have similar units, and displacement current has got into with itself magnetic field just similar to actual currents.

Here,  

$\frac {\epsilon _0 d\phi_E}{dt} = \frac {\epsilon _0 EA}{dt4\pi \varepsilon _0 r^2}$

= $\frac {M^-^1L^-^3T^4A^2}{M^-^1L^-^3A^2} \times \frac {A^1T^1}{L^2} \times \frac {L^2}{T}$

= $A^1$

which can be called as equivalent to current.