Question

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.

Answer 1

The average value of energy density `("energy"//"volume")` is given by
`mu_(av) = (1)/(2)epsi_(0)E_(0)^(2)`
Total volue of the cylinder, ` V = A -1`
`:. ` Total energy contained in the cylinder,
`u = (u_(av))(V) = (1/(2)epsi_(0)E_(0)^(2)) (Al)`
Substituting the value, we have
`mu = (1)/(2) xx (8.86 xx 10^(-12)) (50)^(2)(10 xx 10^(-4)) (50 xx 10^(-2))J`
`= 5.5 xx 10^(-12) J`