A circular parallel plate capacitor with plate radius `R` is charged by means of a cell, at time `t=0`. The initial conduction current is `i_(0)`. Consider a circular area of radius `R//4` coplanar with the capacitor plates and located symmetrically between them. Find the time rate of electric flux change through this area after one time constant.

Explanation

To solve the problem of finding the time rate of electric flux change through a circular area of radius \( \frac{R}{4} \) coplanar with the capacitor plates after one time constant, we can follow these steps:

### Step 1: Understand the Current Decay in the Capacitor
The current \( i(t) \) in the capacitor decreases exponentially over time. The expression for the current at any time \( t \) is given by:
\[ i(t) = i_0 e^{-\frac{t}{\tau}} \]
where \( i_0 \) is the initial conduction current and \( \tau \) is the time constant.
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