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The electric field of a plane electromag...

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 magentic field is (in `Jm^-3`)

A

`12.29 xx 10 ^(-12)`

B

`8.86 xx 10 ^(-12)`

C

`17.72 xx 10 ^(-12)`

D

`4.43 xx 10 ^(-12)`

Text Solution

Verified by Experts

The correct Answer is:
B
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))" " (becauseB _(0) = (E _(0))/( c ))`
` =1/4 epsi _(0) E_(0) ^(2) " "(because c = (1)/( sqrt ( mu _(0) epsi _(0)))`
`=1/4 xx 8.854 xx 10 ^(-12) xx (2) ^(2)`
`= 8.8 54 xx 10 ^(-12) J m ^(-3) ~~ 8.86 xx 10 ^(-12) J m ^(-3)`
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