For an electromagnetic wave, the relationship between electric and magnetic field amplitudes is B0=cE0.
Here E0=54 V/m and c=3×108 m/s.
So, B0=3×10854=1.8×10−7 T.
The electric field is along the j^ direction.
Since the wave travels in the +z direction, the magnetic field direction is determined by E×B pointing in the +z direction.
Using the right-hand rule: j^×(−i^)=k^ (positive z direction), confirming the magnetic field is in the −i^ direction.
Therefore, B=−1.8×10−7sin(kz−ωt)i^ T.