Two infinitely large sheets having charge densities `sigma_(1)andsigma_(2)` respectively `(sigma_(1)gtsigma_(2))` are placed near each other separated by distance 'd'. A small charge 'q' is placed in between two plates such that there is no effect on charge distribution on plates. Now this charge is moved at an angle of `45^(@)` with the horizontal towards plate having charge density `sigma_(2)` by distance 'a' `(altltd)`. Find the work done by electric field in the process.

Explanation

To solve the problem step by step, we will calculate the work done by the electric field when a charge \( q \) is moved between two charged plates.

### Step 1: Understand the Electric Field Between the Plates
The electric field \( E \) between two infinitely large sheets with surface charge densities \( \sigma_1 \) and \( \sigma_2 \) (where \( \sigma_1 > \sigma_2 \)) is given by:
\[ E = \frac{\sigma_1 - \sigma_2}{2 \epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space.
...