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In a plane e.m. wave, the electric field...

In a plane e.m. wave, the electric field oscillates withe amplitude `20Vm^-1`. Find (a) energy density of electric field (b) energy density of magnetic field.

A

`8.86 xx 10 ^(-12)`

B

`4.43 xx 10 ^(-12)`

C

`17.72 xx 10 ^(-12)`

D

`2.21 xx 10 ^(-12)`

Text Solution

Verified by Experts

The correct Answer is:
D
The average eneergy density due to magnetic field
`u _(B) =1/2 (B _(rms)^(2))/( mu _(0)) = (1)/( 2mu _(0)) (( B _(0))/( sqrt2 ) ) ^(2) " "(because B _(rms) = (B _(0))/( sqrt2 ))`
`1/4 (B _(0) ^(2))/( mu _(0)) = 1/4 ((E _(0) //c) ^(2))/( mu _(0))" "(because B _(0) = (E _(0))/( c ))`
`=1/4 (E _(0) ^(2))/( c ^(2) mu _(0)) = (1)/( 4 mu _(0)) = (E _(0) ^(2))/( (1 // mu _(0) epsi _(0))) " " (because c = (1)/( sqrt ( mu _(0) epsi _(0))))`
`=1/4 epsi _(0) E _(0)^(2) =1/4 xx 8.854 xx 10 ^(-12) xx (1) = 2.21 xx 10 ^(-21) J m ^(-3)`
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