Question

A plane electromagnetic wave of electric and magnetic fields \( E_0 \) and \( B_0 \) respectively incidents on a surface. If the total energy transferred to the surface in a time of \( t \) is \( U \), then the magnitude of the total momentum delivered to the surface for complete absorption is:

• A. \( \frac{U E_0}{B_0} \)
• B. \( \frac{U B_0}{E_0} \)
• C. \( \frac{U}{E_0 B_0} \)
• D. \( \frac{U B_0}{E_0^2} \)

Hint:

The momentum delivered by an electromagnetic wave is given by \( p = \frac{U}{c} \).
- The speed of light relates the electric and magnetic fields as \( c = \frac{E_0}{B_0} \).

Answer 1

The Correct Option is B

The momentum \( p \) associated with an electromagnetic wave is related to its energy by: \[ p = \frac{U}{c} \] where \( c \) is the speed of light. 1. Relation between \( E_0, B_0, \) and \( c \): \[ c = \frac{E_0}{B_0} \] 2. Substituting in momentum formula: \[ p = \frac{U}{c} = \frac{U B_0}{E_0} \] Thus, the correct answer is \(\boxed{\frac{U B_0}{E_0}}\).