Question

Electromagnetic waves of energy flux $ 75 \times 10^4 \, \text{W/m}^2 $ incidents normally on a surface of area $ 40 \, \text{cm}^2 $. If the surface absorbs the flux completely, the total momentum delivered to the surface in one second is: Options:

• A. \( 10^{-2} \, \text{kg·m/s} \)
• B. \( 10^{-3} \, \text{kg·m/s} \)
• C. \( 10^{-4} \, \text{kg·m/s} \)
• D. \( 10^{-5} \, \text{kg·m/s} \)

Hint:

The momentum of electromagnetic waves is related to their energy by \( p = \frac{E}{c} \) for complete absorption.

Answer 1

The Correct Option is D

We need to find the momentum delivered by electromagnetic waves to a surface.
Step 1: Calculate the energy delivered.
Energy flux: \[ I = 75 \times 10^4 = 7.5 \times 10^5 \, \text{W/m}^2 \] Area: \[ A = 40 \, \text{cm}^2 = 0.004 \, \text{m}^2 \] Power: \[ P = I \times A = (7.5 \times 10^5) \times 0.004 = 3000 \, \text{W} \] Energy in 1 second: \[ E = 3000 \, \text{J} \] Step 2: Relate energy to momentum.
For complete absorption: \[ p = \frac{E}{c}, \quad c = 3 \times 10^8 \, \text{m/s} \] \[ p = \frac{3000}{3 \times 10^8} = 10^{-5} \, \text{kg·m/s} \] Final Answer: \[ \boxed{10^{-5}} \]