A parallel- plate capacitor having plate-area A and plate separation d is joined to a battery of emf epsilon and internal resistance R at t=0. Consider a plane surface of area A/2, parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time.

Explanation

To find the displacement current through a plane surface of area \( \frac{A}{2} \) situated symmetrically between the plates of a parallel-plate capacitor connected to a battery, we can follow these steps:

### Step 1: Understand the Electric Field in the Capacitor
The electric field \( E \) between the plates of a parallel-plate capacitor is given by:
\[ E = \frac{Q}{A \epsilon_0} \]
where \( Q \) is the charge on the capacitor, \( A \) is the plate area, and \( \epsilon_0 \) is the permittivity of free space.
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