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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.

Text Solution

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Solution:
The energy density is
` (u_av)=((1/2(varepsilon_0)(E_(0)^2))= (1/2 xx (8.85 xx (10^-12)(C^2)(N^-1)(m^-2)) xx((50 NC^(-1))^2)`
` =1.1 xx (10^-8)J m^(-3).`
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)Jm^-3) xx (5 xx (10^-4)m^3)`
` = 5.5 xx (10^(-12))J.
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