Question

The oscillating electric and magnetic field vectors of an electromagnetic wave are in

• A. The same direction and in phase
• B. The same direction but have a phase difference of \(90^\circ\)
• C. Mutually perpendicular directions and are in phase
• D. Mutually perpendicular directions with a phase difference of \(90^\circ\)

Hint:

For an electromagnetic wave: \[ \vec E \perp \vec B \perp \text{Direction of propagation} \] and \[ E \text{ and } B \text{ are always in phase.} \] If \(E\) is maximum, \(B\) is also maximum at the same instant.

Answer 1

The Correct Option is C

Concept: According to Maxwell's electromagnetic wave theory:
• The electric field \((\vec E)\) and magnetic field \((\vec B)\) are mutually perpendicular.
• Both are perpendicular to the direction of propagation.
• The electric and magnetic fields attain maxima and minima simultaneously. Hence, they oscillate in phase.

Step 1:Recall the orientation of fields in an electromagnetic wave. \[ \vec E \perp \vec B \] and \[ \vec E \perp \text{Direction of propagation} \] \[ \vec B \perp \text{Direction of propagation} \]

Step 2: Recall the phase relationship. For an electromagnetic wave, \[ E=E_0\sin(kx-\omega t) \] \[ B=B_0\sin(kx-\omega t) \] Since both have the same phase term, \[ {\text{Electric and magnetic fields are in phase.}} \]

Step 3: State the answer. \[ { \begin{array}{c} \vec E \text{ and } \vec B \text{ are mutually perpendicular} \text{and oscillate in phase.} \end{array} } \] Hence, the correct option is \[ {(C)} \]