Question

Consider a parallel plate capacitor whose plates are closely spaced. Let R be the radius of the plates and the current in the wire connected to the plates is 5 A, calculate the displacement current through the surface passing between the plates by directly calculating the rate of change of flux of electric field through the surface.

Answer 1

The conduction current I_c = 5A

According to Gauss’s Law,

Electric flux, θ_E = `"q"/epsilon_0`

`"I"_"d" = epsilon * ("d"phi_"E")/"dt"`

`= epsilon_0 "d"/"dt" ("q"/epsilon_0) = epsilon_0/epsilon_0 ("dq"/"dt")`

`"I"_"c" = "q"/"t" => "q" = "I"_"c" "t"`

`"I"_"d" = "d"/"dt" ("I"_"c""t")`

`= "I"_"c" ("d"("t"))/"dt"` = 5A

I_d = I_c = 5A