1. Given data

• Wave propagates in the $+x$-direction.
• Wavelength: $\lambda = 8\text{ mm} = 8\times 10^{-3}\text{ m}$
• Electric field is along $y$-direction.
• Maximum electric field magnitude: $E_0 = 60\,\text{V m}^{-1}$
• Since the wave is in vacuum, speed is $c = 3\times 10^8\,\text{m s}^{-1}$

2. Form of EM wave propagating in $+x$-direction

A sinusoidal EM wave traveling in the $+x$-direction can be written as $E_y = E_0\sin(kx-\omega t)\,\hat j$ $B_z = B_0\sin(kx-\omega t)\,\hat k$

Since $kx-\omega t = k(x-vt)$ for vacuum, $v=c$.

So the argument should be of the form $k(x-ct)$

3. Calculate wave number $k$

$k = \frac{2\pi}{\lambda} = \frac{2\pi}{8\times 10^{-3}}$

$k = \frac{\pi}{4\times 10^{-3}} = \frac{\pi}{4}\times 10^3\,\text{m}^{-1}$

So the phase term is $\left(\frac{\pi}{4}\times 10^3\right)(x-3\times 10^8 t)$

This matches options A, B, and C.

4. Find magnetic field amplitude

For an EM wave in vacuum, $E_0 = cB_0$

Therefore, $B_0 = \frac{E_0}{c} = \frac{60}{3\times 10^8}$

$B_0 = 20\times 10^{-8} = 2\times 10^{-7}\,\text{T}$

5. Direction check

Given:

• $\vec E$ along $\hat j$
• wave propagates along $\hat i$

For EM waves, $\vec E \times \vec B = \text{direction of propagation}$

We need $\hat j \times \hat k = \hat i$

This is correct. So $\vec B$ must be along $\hat k$.

6. Construct the correct fields

Thus, $E_y = 60\sin\left[\left(\frac{\pi}{4}\times 10^3\right)(x-3\times 10^8 t)\right]\hat j\,\text{V m}^{-1}$

$B_z = 2\times 10^{-7}\sin\left[\left(\frac{\pi}{4}\times 10^3\right)(x-3\times 10^8 t)\right]\hat k\,\text{T}$

7. Option-wise check

• A: Magnetic amplitude is $2\,\text{T}$, which is wrong.
• B: Both phase term and amplitudes are correct.
• C: Electric and magnetic amplitudes are interchanged, wrong.
• D: Wrong speed and wrong wave number.

Therefore, the correct option is B.