Question

An electromagnetic wave propagating through vacuum, described by \( E = E_0 \sin(kx - \omega t) \), \( B = B_0 \sin(kx - \omega t) \), then: 
 

• A. \( E_0 k = B_0 \omega \)
• B. \( E_0 \omega = B_0 k \)
• C. \( E_0 B_0 = \omega k \)
• D. \( E_0 B_0 = \sqrt{\omega k} \)

Hint:

The electric and magnetic field amplitudes in an electromagnetic wave are related by the speed of light, \( c = E_0 / B_0 \).

Answer 1

The Correct Option is B

For an electromagnetic wave, the electric and magnetic field strengths \( E_0 \) and \( B_0 \) are related by the speed of light in vacuum \( c \): \[ E_0 = c B_0. \] The wave number \( k \) and angular frequency \( \omega \) are related to the speed of light as: \[ c = \frac{\omega}{k}. \] Combining the two equations, we get: \[ E_0 \omega = B_0 k. \]