Separation between the plates of a capacitor is increased from d to 2d while the battery remains connected with the plates. How will the stored energy in the capacitor change?

Explanation

To solve the problem of how the stored energy in a capacitor changes when the separation between the plates is increased from \( d \) to \( 2d \) while the battery remains connected, we can follow these steps:

### Step 1: Understand the initial conditions
We start with a capacitor connected to a battery. The capacitance \( C \) of a parallel plate capacitor is given by the formula:
\[ C = \frac{A \epsilon_0}{d} \]
where:
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