The electric field of a plane electromagnetic wave varies with time of amplitude `2Vm^-1` propagating along z-axis. The average energy density of the magnetic field is (in `Jm^-3`)

Options

A. `13.29xx10^(-12)`
B. `8.86xx10^(-12)`
C. `17.72xx10^(-12)`
D. `4.43xx10^(-12)`

Answer

B

Explanation

Amplitude of electric field and magnetic field are related by the relation
`(E_(0))/(B_(0)) = c`
Average energy density of the magnetic field is
`u_(B) = (1)/(4) (B_(0)^(2))/(mu_(0)) = (1)/(4) (E_(0)^(2))/(mu_(0)c^(2)) ( :' B_(0) = (E_(0))/(c))`
` =(1)/(4) epsilon_(0)E_(0)^(2) ( :' c = (1)/(sqrt(mu_(0)epsilon_(0))))`
`= (1)/(4) xx 8.854 xx 10^(-12) xx (2)^(2) = 8.854 xx 10^(-12) J m^(-3)`
`~~ 8.86 xx 10^(-12) J m^(-3)`