A parallel plate capacitors of plate area A has a total surface charge density `+sigma` on one plate and a total surface charge density `-sigma` on the other plate. The force one plate due to the other plate is given by :

Options

A. `(sigma^(2)A^(2))/(2epsi_(0))`
B. `(sigma^(2)A^(2))/(epsi_(0))`
C. `(sigma^(2)A)/(2epsi_(0))`
D. `(sigma^(2)A)/(epsi_(0))`

Explanation

To solve the problem of finding the force on one plate of a parallel plate capacitor due to the other plate, we can follow these steps:

### Step-by-Step Solution

1. **Identify the Charge on Each Plate**:
- The surface charge density on the first plate is given as \( +\sigma \).
- The surface charge density on the second plate is given as \( -\sigma \).
- The area of each plate is \( A \).
- Therefore, the total charge on the first plate, \( Q_1 \), is:
\[ Q_1 = \sigma \cdot A \]
- The total charge on the second plate, \( Q_2 \), is:
\[ Q_2 = -\sigma \cdot A \]

2. **Calculate the Electric Field Due to One Plate**:
- The electric field \( E \) produced by a single plate with surface charge density \( \sigma \) is given by:
\[ E = \frac{\sigma}{2\epsilon_0} \]
- Since we are interested in the electric field produced by the second plate (which has charge density \( -\sigma \)), the electric field at the location of the first plate (due to the second plate) is:
\[ E = \frac{-\sigma}{2\epsilon_0} \]
- However, since we are calculating the force on the first plate, we will consider the magnitude of the electric field:
\[ E = \frac{\sigma}{2\epsilon_0} \]

3. **Calculate the Force on the First Plate**:
- The force \( F \) on the first plate due to the electric field from the second plate can be calculated using the formula:
\[ F = E \cdot Q_1 \]
- Substituting the values we have:
\[ F = \left(\frac{\sigma}{2\epsilon_0}\right) \cdot (\sigma \cdot A) \]
- Simplifying this gives:
\[ F = \frac{\sigma^2 A}{2\epsilon_0} \]

4. **Determine the Nature of the Force**:
- Since the first plate has a positive charge and the second plate has a negative charge, the force will be attractive.

### Final Answer
The force on one plate due to the other plate is given by:
\[ F = \frac{\sigma^2 A}{2\epsilon_0} \]