To solve this problem, we need to find the peak value of the magnetic field $B_0$ in an electromagnetic wave.$\\$Given:$\\ E_{rms} = 6$ V/m$\\$The relationship between the root mean square (rms) value and the peak value of the electric field is:$\\ E_{rms} = \frac{E_0}{\sqrt{2}} \\$where $E_0$ is the peak value of the electric field.$\\$Rearranging the equation to solve for $E_0: \\ E_0 = E_{rms} \cdot \sqrt{2} \\$Substitute the given value:$\\ E_0 = 6 \cdot \sqrt{2}$ V/m$\\ E_0 = 6 \cdot 1.414$ V/m$\\ E_0 \approx 8.484$ V/m$\\$In free space, the relationship between the electric field $E_0$ and the magnetic field $B_0$ is given by:$\\ E_0 = c \cdot B_0 \\$where $c$ is the speed of light in vacuum, approximately $3 \times 10^8$ m/s.$\\$Rearrange to solve for $B_0: \\ B_0 = \frac{E_0}{c} \\$Substitute the known values:$\\ B_0 = \frac{8.484}{3 \times 10^8}$ T$\\ B_0 \approx 2.828 \times 10^{-8}$ T$\\$Therefore, the peak value of the magnetic field is approximately $2.83 \times 10^{-8}$ T.$\\$This corresponds to Option 1.