To find the amplitude of the oscillating magnetic field in a plane electromagnetic wave, we use the relationship between the electric field $(E)$ and the magnetic field $(B)$ in free space.$\\ \\$The relationship is given by:$\\ E = c \cdot B \\ \\$where $c$ is the speed of light in free space.$\\ \\$Given:$\\ E = 48 \, \mathrm{V/m} \\ c = 3 \times 10^8 \, \mathrm{m/s} \\ \\$We need to find $B. \\ \\$Rearrange the equation to solve for $B: \\ B = \frac{E}{c} \\ \\$Substitute the known values:$\\ B = \frac{48}{3 \times 10^8} \\ \\$Calculate $B: \\ B = 16 \times 10^{-8} \, \mathrm{T} \\ \\$Therefore, the amplitude of the oscillating magnetic field is $1.6 \times 10^{-7} \, \mathrm{T}. \\ \\$This corresponds to Option 3.