A plane e.m. wave propagating in the x-direction has a wavelength 5.5 mm. The electric field is in the y-direction and its maximum magitude is `36Vm^_1`. Write suitable equation for the electric and magnetic fields as a function of x and t and find energy density of e.m. wave. Calculate the maximum electric and magnetic force on a charge q=2e, moving along y-axis with a speed of `3.0xx10^7ms^-1`, where `e=1.6xx10^(-19)C`.

Answer

`E_y=36 sin 1.14 xx10^(11)[t-x//c] V//m ; B_z=1.2xx10^(-7)sin 1.14xx10^(11)(t-x//c)T and 5.7xx10^-9 Jm^-3`

Explanation

Here, `lambda=5.5mm=5.5xx10^-3m, E_0=36V//m^-1`
`omega=2piv=(2pic)/lambda=(2xx3.14xx(3xx10^8))/(5.5xx10^-3)`
`1.14xx10^(11)rad//s`
`B_0=(E_0)/c=36/(3xx10^8)=1.2xx10^-7T`
The equation for the electric field, along y-axis will be
`E=E_y=E_0 sin omega(t-x/c)`
`=36sin 1.14xx10^(11)(t-x//c) Vm^-1`
The equation for the magnetic field along z-axis
`B=B_z=B_0 sin omega(t-x/c)`
`=1.2xx10^-7 sin 1.14xx10^(11)(t-x//c)T`
Average energy density of e.m. wave is
`u=1/2 epsilon_0 E_0^2=1/2xx(8.85xx10^(-12))xx(36)^2`
`=5.7xx10^-9Jm^-3`