In a plane electromagnetic wave, the electric field of amplitude `1 Vm^(-1)` varies with time in free space. The average energy density of electric field is (in `Jm^(-3)`)

Options

A. `8.86 xx 10 ^(-12)`
B. `4.43 xx10 ^(-12)`
C. `1.11 xx 10 ^(-12)`
D. `2.21 xx 10 ^(-12)`

Answer

D

Explanation

We know
The energy density (energy per unit volume) in an electric field E in vacuum
`=1/2 epsi _(0) E ^(2)`
`U = 1/2 epsi _(0) E ^(2)`
where `epsi _(0) = 8.86 xx 10 ^(-12) C ^(2) //N -m ^(2)`
`E = 1 V//m`
`=1/2 xx 8.86 xx 10 ^(-12) xx (1)^(2)`
`= 4.43 xx 10 ^(-12)`
So, the average enegy density of magnetic field
`= ( 4.43 xx 10 ^(-12))/( 2)`
`= 2.21 xx 10 ^(-12) J//m ^(2)`