The rms value of the electric field of the light from the sun is `720 N//C` The total energy density of the electromagnetic wave is

Options

A. `3.3 xx 10 ^(-3) J m ^(-3)`
B. `4.58 xx 10 ^(-6) J m ^(-3)`
C. `7.37 xx 10 ^(-9) J m ^(-3)`
D. `81.35 xx 10 ^(-12) J m ^(-3).`

Answer

B

Explanation

Total average energy density of electromagnetic wave is
`u =1/2 epsi _(0) E _(rms ) ^(2) + (1)/( 2mu _(0)) B _(rm s) ^(2)`
`=1/2 epsi _(0) E _(rms ) ^(2) + (1)/( 2mu _(0)) ((E _(rms ) ^(2))/( c ^(2))) (because B _(rms ) = (E _(rms ))/( c ))`
`=1/2 epsi _(0) E _(rms ) ^(2) + (1)/( 2mu _(0) ) E _(rm s ) ^(2) epsi _(0) mu _(0)" "(because c = (1)/( sqrt ( mu _(0) epsi _(0))))`
`=1/2 epsi _(0) E _(rms ) ^(2) + 1/2 epsi _(0) E _(rms) ^(2) = epsi _(0) E_(rms) ^(2)`
`= (8.85 xx 10 ^(-12)) xx (720) ^(2) = 4. 58 xx 10 ^(-6) J m ^(-3)`