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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.
Solution
The conduction current Ic = 5A
According to Gauss’s Law,
Electric flux, θE = `"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
Id = Ic = 5A
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