1. Given data

• Frequency: $\nu = 23.9\,\text{GHz} = 23.9 \times 10^9\,\text{Hz}$
• Peak electric field: $E_0 = 60\,\text{V/m}$
• Wave propagates along $+z$ direction in free space.

We need the correct magnetic field component $\vec B$.

2. Magnitude of magnetic field

For an electromagnetic wave in free space,

$E_0 = c B_0$

So,

$B_0 = \frac{E_0}{c} = \frac{60}{3 \times 10^8} = 2 \times 10^{-7}\,\text{T}$

Thus the magnetic field must have amplitude

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

This rules out option B, since its amplitude is wrong.

3. Direction of magnetic field

For an EM wave,

$\vec E \perp \vec B \perp \text{direction of propagation}$

Since propagation is along $+z$, both $\vec E$ and $\vec B$ must lie in the $xy$-plane.

So $\vec B$ cannot be along $\hat{k}$. Hence B is invalid.

Options C and D have $\vec B$ along $\hat{i}$, which is acceptable. Option A has $\vec B$ along $\hat{j}$, also in principle acceptable, but we must check the phase and propagation form.

4. Wave number and angular frequency

Angular frequency:

$\omega = 2\pi \nu = 2\pi (23.9 \times 10^9) \approx 1.5 \times 10^{11}\,\text{rad/s}$

Wave number:

$k = \frac{\omega}{c} = \frac{1.5 \times 10^{11}}{3 \times 10^8} = 0.5 \times 10^3\,\text{rad/m}$

So the magnetic field should contain

$\sin(kz - \omega t)$

or equivalently any phase-equivalent form for propagation along $+z$.

5. Condition for propagation along $+z$

A wave traveling along $+z$ has phase of the form

$kz - \omega t$

A wave with phase $kz + \omega t$ travels along $-z$.

Now check options:

• A: $\sin(1.5\times10^2 x + 0.5\times10^{11} t)\,\hat j$
  • Depends on $x$, not $z$ $\Rightarrow$ wrong propagation variable.
• C: $\sin(0.5\times10^3 z + 1.5\times10^{11} t)\,\hat i$
  • Has $kz + \omega t$ $\Rightarrow$ propagates along $-z$.
• D: $\sin(0.5\times10^3 z - 1.5\times10^{11} t)\,\hat i$
  • Correct form for propagation along $+z$.

Thus D is the acceptable magnetic field component.

6. Final answer

The correct option is

$\boxed{\text{D}}$