Two equal charges, `2.0xx10^(-7) C` each, are held fixed at a separation of 20cm. A third charge of equal magnitude is placed midway between the two both the charges. How much work is done by the electric field during the process?

Explanation

To solve the problem, we need to calculate the work done by the electric field when a third charge is placed midway between two equal charges. Here’s a step-by-step solution:

### Step 1: Understand the Initial Setup
We have two fixed charges, each of magnitude \( q = 2.0 \times 10^{-7} \, C \), separated by a distance \( r = 20 \, cm = 0.2 \, m \). The third charge, also of the same magnitude \( q \), is placed midway between the two charges.

### Step 2: Calculate the Initial Potential Energy (E1)
Initially, only the two charges are present. The potential energy \( E_1 \) of the system can be calculated using the formula for the potential energy between two point charges:
\[
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