A plane electromagnetic wave has frequency of $2.0 \times 10^{10}\ \text{Hz}$ and its energy density is $1.02 \times 10^{-8}\ \text{J m}^{-3}$ in vacuum. The amplitude of the magnetic field of the wave is close to $\left(\dfrac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\ \dfrac{\text{N m}^{2}}{\text{C}^{2}}\right.$ and speed of light $\left.= 3 \times 10^{8}\ \text{m s}^{-1}\right)$
Answer: (B) $160\ \text{nT}$
Average energy density (electric + magnetic) of the wave is $u = \dfrac{B_0^{2}}{2\mu_0}$.
$$B_0 = \sqrt{2\mu_0 u} = \sqrt{2\times4\pi\times10^{-7}\times1.02\times10^{-8}} \approx 1.6\times10^{-7}\ \text{T} = 160\ \text{nT}$$
($\mu_0 = 1/(\varepsilon_0 c^{2}) = 4\pi\times10^{-7}$ follows from the given data.)
Solution by Sreeraj P, M.Sc Physics