Question

The electric field in an electromahetic wave is given by `E = 100sin omega (t-x//c)`. Find the energy contained in a cylinder of crross section `20cm^(2)` and length `1 m` along the `x`-axis. Also find intensity of wave.

Answer 1

The energy density
`u_(av) = (1)/(2)in_(0)E_(0)^(2)`
The volume of cylinder `V = Al`
The enegry contained in this volume
`U = u_(av) V = (1)/(2)in_(0)E_(0)^(2)Al`
`= (1)/(2)(8.85 xx 10^(-12)) (100)^(2)(20 xx 10^(-4))(1)`
`= 8.85 xx 10^(-11) J`
The intensity of wave is
`I = (1)/(2)in_(0)E_(0)^(2)c`
`= (1)/(2)(8.85 xx 10^(-12))(100)^(2)(3xx 10^(8))`
`= 13.3 W//m^(2)`