Question

Consider the following statements regarding a plane wave propagating through free space. The direction of field :
• [A.] \(\vec{E}\) is perpendicular to the direction of propagation.
• [B.] \(\vec{H}\) is perpendicular to the direction of propagation.
• [C.] \(\vec{E}\) is perpendicular to the direction of field \(\vec{H}\). Choose the correct answer from the options given below :

• A. A and B Only
• B. B and C Only
• C. A and C Only
• D. A, B and C Only

Hint:

For electromagnetic plane waves: \[ \vec{E}\perp \vec{H}\perp \text{direction of propagation} \] Thus EM waves are transverse in nature.

Answer 1

The Correct Option is D

Concept: An electromagnetic plane wave propagating in free space is a: \[ \text{Transverse Electromagnetic (TEM) wave} \] For TEM waves:
• Electric field \(\vec{E}\) is perpendicular to propagation direction.
• Magnetic field \(\vec{H}\) is perpendicular to propagation direction.
• Electric field \(\vec{E}\) is perpendicular to magnetic field \(\vec{H}\). The three vectors satisfy: \[ \vec{E}\perp \vec{H}\perp \vec{k} \] where: \[ \vec{k}=\text{direction of propagation} \]

Step 1: Analyze statement A. Statement A says: \[ \vec{E}\text{ is perpendicular to propagation direction} \] This is true because electromagnetic waves are transverse waves. Thus: \[ A \text{ is correct} \]

Step 2: Analyze statement B. Statement B says: \[ \vec{H}\text{ is perpendicular to propagation direction} \] This is also true for TEM waves. Hence: \[ B \text{ is correct} \]

Step 3: Analyze statement C. Statement C says: \[ \vec{E}\perp \vec{H} \] This is again true because electric and magnetic fields are mutually perpendicular. Thus: \[ C \text{ is correct} \]

Step 4: Conclude the correct option. All three statements are correct. Therefore: \[ A,\ B,\ C \] are true.

Step 5: Write the final answer. Hence, the correct option is: \[ \boxed{(D)\ A,\ B \text{ and } C \text{ Only}} \]