The momentum carried by E-M waves in vaccum is P, then energy associated with the wave is equal to (C) is speed of light)

Options

A. `pxxc`
B. `(Pc)/(-2)`
C. `(P^(2))/(2c)`
D. `(P)/(c)`

Answer

To solve the problem, we need to find the energy associated with electromagnetic (E-M) waves in vacuum given their momentum \( P \).

### Step-by-Step Solution:

1. **Understand the relationship between momentum and energy**:
The momentum \( P \) of an electromagnetic wave is related to its energy \( E \) and the speed of light \( c \). We can use the formula:
\[ P = \frac{E}{c} \]

2. **Rearranging the formula**:
To find the energy \( E \), we can rearrange the above formula:
\[ E = P \cdot c \]

3. **Identify the correct option**:
From the rearranged formula, we see that the energy associated with the electromagnetic wave is equal to the momentum multiplied by the speed of light. Therefore, the answer is:
\[ E = P \cdot c \]

4. **Check the options**:
The options provided were:
- Option 1: \( P \cdot c \)
- Option 2: \( \frac{P \cdot c}{2} \)
- Option 3: \( \frac{P^2}{2c} \)
- Option 4: \( \frac{P}{c} \)

The correct answer matches with Option 1: \( P \cdot c \).

### Final Answer:
The energy associated with the electromagnetic wave is \( E = P \cdot c \).

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