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The electric field in an electromagnetic...

The electric field in an electromagnetic wave is given by `E=( 50N (C^-1)) sin omega (t-x/c).` Find the energy contained in a cylinder of cross section `10 cm^2` and length 50 cm along the x- axis.

A

The volume of the cylinder is `5 xx 10 ^(-4) m ^(3)`

B

The energy contained in cylinder is `5.5 xx 10 ^(-12) J`

C

The volume of the cylinder is `3 xx 10 ^(7) m ^(3)`

D

The energy contained in cylinder is `7 xx 10 ^(-12) J`

Text Solution

Verified by Experts

The correct Answer is:
A, B
The energy density is
`u _(av) = 1/2 epsi _(0) E _(0) ^(2)`
`=1/2 xx (8.85 xx 10 ^(-12) C ^(2) N ^(-1) m ^(-2)) xx (50 N C ^(-1)) ^(2)`
`=1.1 xx 10 ^(-8) J m ^(-8)`
The volume of the cylinder is
`V=10 cm^(2) xx 50 cm = 5 xx 10 ^(-4) m ^(3)`
The energy contained in this volume is
`U = (1.1 xx 10 ^(-8) J m ^(-3)) xx (5 xx 10 ^(-4) m ^(3)) = 5.5 xx 10 ^(-12) J`
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