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asymptotically
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Homework Statement
Hi, the problem is to calculate the the displacement current flowing through a surface that lies in between the two plates of a parallel plate capacitor as the capacitor discharges. I think I have a correct solution but I'm not 100% sure on why it's correct.
Homework Equations
Gauss Law: [itex]\oint_S E \cdot dA=\frac{Q_{enc}}{\epsilon_0} [/itex]
Definition of Displacement Current: [itex]I_d=\epsilon_0\frac{d}{dt}\oint_S E \cdot dA[/itex]
The Attempt at a Solution
Constructing a Gaussian surface about one of the plates like this we have [itex]\oint_S E \cdot dA=\frac{Q(t)_C}}{\epsilon_0} [/itex].
Now this is the part I'm slightly confused about, the flux through every surface except the surface
that lies in between the plates has to be zero, why is there no flux through the left surface. Also we also only consider the charge on the capacitor and ignore the charge in the wire? Are these simplifications or is there justification for this.
The answer for [itex]I_d[/itex] is then just derivative of the rate of change of the charge on the capacitor which is the conduction current.