A plane electromagnetic wave is moving in free space with velocity...

For an electromagnetic wave, the relationship between electric and magnetic field amplitudes is $B_0 = \frac{E_0}{c}$.
Here $E_0 = 54$ V/m and $c = 3 \times 10^8$ m/s.
So, $B_0 = \frac{54}{3 \times 10^8} = 1.8 \times 10^{-7}$ T.
The electric field is along the $\hat{j}$ direction.
Since the wave travels in the $+z$ direction, the magnetic field direction is determined by $\vec{E} \times \vec{B}$ pointing in the $+z$ direction.
Using the right-hand rule: $\hat{j} \times (-\hat{i}) = \hat{k}$ (positive $z$ direction), confirming the magnetic field is in the $-\hat{i}$ direction.
Therefore, $\vec{B} = -1.8 \times 10^{-7}\sin(kz - \omega t)\hat{i}$ T.