Question

Show that the dimensions of the displacement current `∈_0 (d varphi_E)/dt` are that of an electric current .

Answer 1

Displacement current,

`I_D = (∈_0 d varphi_e)/dt`

Electric flux,

`Ø_e = EA`

`[Ø_e] = [E] [A]`

= `[1/(4pi∈_0) q/r^2] [A]`

Also , `[∈_0] = [M^-1L^-3 T^4 A^2]`

⇒ `[Ø_e] = [M^1L^3T^-4A^-2] [AT][L^-2][L^2]`

= `[ML^3T^-3A^-1]`

Displacement current,

`[I_D] = [∈_0] [Ø_e] [T^-1]`

`[I_D] = [M^-1L^-3T^4A^2] [ML^3T^-3A^-1][T^-1]`

`[I_D] = [A]`

`[I_D] = ["Current"]`