Question

The electric field for an electromagnetic wave is given by \( E = 40 \sin(kz - 6 \times 10^8 t) \), where the magnitude of \( E_0 \) is in V/m.
The magnitude of the wave vector \( k \) is 
 

• A. 8 rad/m
• B. 4.5 rad/m
• C. 2 rad/m
• D. 12 rad/m

Hint:

The wave vector \( k \) is related to the angular frequency and the speed of light, and determines the spatial frequency of the wave.

Answer 1

The Correct Option is C

The electric field for an electromagnetic wave is given as: \[ E = E_0 \sin(kz - \omega t) \] Where:
\( E_0 = 40 \, {V/m} \) is the magnitude of the electric field,
\( k \) is the wave vector,
\( \omega = 6 \times 10^8 \, {rad/s} \) is the angular frequency.
The wave number \( k \) is related to the angular frequency \( \omega \) by the equation: \[ k = \frac{\omega}{c} \] Where \( c = 3 \times 10^8 \, {m/s} \) is the speed of light. Substituting the values: \[ k = \frac{6 \times 10^8}{3 \times 10^8} = 2 \, {rad/m} \] 
Final Answer: 2 rad/m.