1. Use the relation between $\vec E$, $\vec B$, and direction of propagation

For a plane electromagnetic wave in free space:

$E = cB$

and the direction of propagation is along

$\vec E \times \vec B$

Given:

• Wave travels along the $+X$-direction
• $\vec E = 9.6\,\hat{j}\,\text{V/m}$

So we need $\vec B$ such that

$\hat{j} \times \vec B = \hat{i}$

Using unit vectors:

$\hat{j} \times \hat{k} = \hat{i}$

Hence, magnetic field must be along $\hat{k}$.

2. Find the magnitude of $\vec B$

Using

$B = \frac{E}{c}$

with $c = 3 \times 10^8\,\text{m/s}$:

$B = \frac{9.6}{3 \times 10^8} = 3.2 \times 10^{-8}\,\text{T}$

3. Write the magnetic field vector

Therefore,

$\vec B = 3.2 \times 10^{-8}\,\hat{k}\,\text{T}$

4. Check options

• A: wrong magnitude and wrong direction
• B: wrong direction
• C: wrong magnitude
• D: correct

So the correct option is D.

5. Comparison with stored answer

Stored correct answer: D

My derived answer: D

They match.