Question

The electric and magnetic fields associated with an electromagnetic wave propagating along \(+z\) axis, can be represented by

• A. \(E = E_0\hat{i}, \quad B = B_0\hat{j}\)
• B. \(E = E_0\hat{i}, \quad B = B_0\hat{k}\)
• C. \(E = E_0\hat{k}, \quad B = B_0\hat{j}\)
• D. \(E = E_0\hat{j}, \quad B = B_0\hat{k}\)

Hint:

Use \( \vec{E} \times \vec{B} = \text{direction of propagation} \) to quickly identify correct orientation.

Answer 1

The Correct Option is A

Step 1: Direction of propagation.
Wave is propagating along \(+z\)-axis.

Step 2: Nature of electromagnetic waves.
Electric field, magnetic field and direction of propagation are mutually perpendicular.

Step 3: Right-hand rule.
\[ \vec{E} \times \vec{B} = \vec{k} \]

Step 4: Check option (A).
\[ \hat{i} \times \hat{j} = \hat{k} \] This matches propagation along \(+z\)-axis.

Step 5: Reject other options.
Other combinations do not satisfy perpendicularity or correct cross product direction.

Step 6: Final conclusion.
\[ \boxed{E = E_0\hat{i}, \quad B = B_0\hat{j}} \] Hence, correct answer is option (A).