A plane electromagnetic wave is incident on a plane surface of area A, normally and is perfectly reflected. If energy E strikes the surface in time t then average pressure exerted on the surface is (c = speed of light)

Options

A. Zero
B. `(E )/("Atc")`
C. `(2 E)/("Atc")`
D. `( E)/(c )`

Answer

To solve the problem of finding the average pressure exerted on a surface by a perfectly reflected electromagnetic wave, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have a plane electromagnetic wave striking a surface of area \( A \) normally (perpendicularly).
- The energy \( E \) strikes the surface in time \( t \).
- We need to find the average pressure exerted on the surface.

2. **Relating Energy to Momentum**:
- The energy \( E \) of the electromagnetic wave can be related to momentum. The momentum \( P \) of the wave can be expressed as:
\[ P = \frac{E}{c} \]
- Here, \( c \) is the speed of light.

3. **Change in Momentum upon Reflection**:
- When the wave is reflected, the change in momentum \( \Delta P \) can be calculated. The initial momentum before reflection is \( P \) (downward) and the final momentum after reflection is \( -P \) (upward).
- Thus, the change in momentum is:
\[ \Delta P = P_{\text{final}} - P_{\text{initial}} = -P - P = -2P \]
- Substituting for \( P \):
\[ \Delta P = -2 \left(\frac{E}{c}\right) = \frac{2E}{c} \]

4. **Calculating Average Force**:
- The average force \( F_{\text{avg}} \) exerted on the surface can be calculated using the change in momentum over time:
\[ F_{\text{avg}} = \frac{\Delta P}{\Delta t} = \frac{2E/c}{t} = \frac{2E}{ct} \]

5. **Calculating Average Pressure**:
- Pressure \( P \) is defined as force per unit area. Therefore, the average pressure \( P_{\text{avg}} \) exerted on the surface is:
\[ P_{\text{avg}} = \frac{F_{\text{avg}}}{A} = \frac{2E/(ct)}{A} = \frac{2E}{A ct} \]

### Final Result:
The average pressure exerted on the surface is:
\[ P_{\text{avg}} = \frac{2E}{A ct} \]