A plane e.m. wave propagating in the x-direction has a wavelength 5.0 mm. The electric field is in the y-direction and its maximum magitude is `50Vm^_1`. Write the equation for the electric and magnetic fields as a function of x and t.

Answer

`E_y=50 sin 3.77xx10^(11)[t-x//c]Vm^-1 ; B_z=1.67xx10^-7 sin 3.77xx10^(11)(t-x//c)tesla`

Explanation

Here, `lambda=5.0mm=5xx10^-3m,`
`E_0=50Vm^-1`
Angular frequency `omega=2piv`
`=(2pic)/(lambda)=(2xxpixx3xx10^8)/(5xx10^-3)=3.77xx10^(11) rad s^-1`
`B_0=(E_0)/c=50/(3xx10^8)=1.67xx10^-7T`
The equation for the electric field along y-axis
is `E_y=E_0sin omega(t-x//c)`
`=50sin 3.77xx10^(11)(t-x//c)Vm^-1`
The equation for the magnetic field along z-axis
`B_z=B_0sin omega(t-x//c)`
`=1.67xx10^-7 sin 3.77xx10^(11)(t-x//c)Vm^-1 tesla`