The electric field of a plane electromagnetic wave varies with time of amplitude $2 V{m}^{-1}$ propagating along z-axis. The average energy density of the magnetic field is( in $J{m}^{-3}$ )

Average energy density of magnetic field$=\frac{{\left(B_{rms}\right)}^2}{2{\mu }_0}=\frac{{(B_0/\sqrt{2})}^2}{2{\mu }_0}=\frac{1}{4}\frac{B_0^2}{{\mu }_0}$

But $B_0=\frac{E_0}{C}$

Average energy density of magnetic field is$\frac{1}{4}\frac{E_0^2}{C^2{\mu }_0}=\frac{1}{4}{\in }_0{E}_0^2 \left(\therefore {\in }_0=\frac{{\displaystyle 1}}{{\displaystyle C^2{\mu }_0}}\right)$

Average energy density of magnetic field $=\frac{1}{4}\times 8.85\times {10}^{-12}\times 2^2=8.85\times {10}^{-12}J/m^3$