Question

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 magnetic field ( J $m^{-1}$ ) is

• A. $13.29{10}^{-12}$
• B. $8.86{10}^{-12}$
• C. $17.72{10}^{-12}$
• D. $4.43{10}^{-12}$

Answer 1

The correct option is C $17.72{10}^{-12}$

Average energy density of the magnetic field is

$U_B=\frac{1}{2}\frac{B_0^2}{{\mu }_0}=\frac{1}{2}\frac{E_0^2}{{\mu }_0{c}^2}$ $(\therefore B_0=\frac{E_0}{c})$

$⟹U_B=\frac{1}{2}{ϵ}_0{E}_0^2$

$⟹U_B=\frac{1}{2}\times 8.854\times {10}^{-12}\times (2{)}^2⟹U_B=17.708\times {10}^{-12}J{m}^{-3}$