To solve this problem, we need to use the properties of electromagnetic (EM) waves.$\\$In an EM wave, the electric field $(\mathbf{E}),$ magnetic field $(\mathbf{B}),$ and the direction of propagation $(\mathbf{V}) \\$are mutually perpendicular to each other.$\\$Given:$\\$• The velocity of the EM wave is $\mathbf{V} = V \hat{i}$ (along the $+x$ axis).$\\$• The electric field $\mathbf{E}$ is along the $+y$ axis.$\\$We need to find the direction of the magnetic field $\mathbf{B}. \\$According to the right-hand rule for EM waves:$\\$• Point your thumb in the direction of wave propagation $(\mathbf{V}). \\$• Point your index finger in the direction of the electric field $(\mathbf{E}). \\$• Your middle finger, perpendicular to both, will point in the direction of the magnetic field $(\mathbf{B}). \\$Applying this rule:$\\$• Thumb points along $+x$ (direction of $\mathbf{V}). \\$• Index finger points along $+y$ (direction of $\mathbf{E}). \\$The middle finger will then point along the $+z$ axis, indicating the direction of $\mathbf{B}. \\$Therefore, the direction of the oscillating magnetic field is along the $+z$ direction.$\\$This corresponds to Option 2.