The magnetic field in a plane electromagnetic wave is given by `B_(y) = 2xx10^7 T sin (0.5xx10^3x+1.5xx10^11 t) T`
(a) What is the wavelength and frequency of the wave?
(b) Write an expression for the electric field.

Explanation

(a) Comparing the given equation with the equation of magnetic field varying sinosoidally with
x and t as
`B_y=B_0sin omega(t+x/c) = B_0sin .(2pi)/T (t+x/c) =B_0sin .((2pi)/T t +(2pi)/T x/c) = B_0 sin .((2pix)/(lambda)+(2pit)/T)`
we get, `(2pi)/(lambda)=0.5xx10^3 or lambda=(2pi)/(0.5xx10^3)m=1.26xx10^-2m and (2pi)/T=1.5xx10^11`
or `2piv=1.5xx10^11 or v=(1.5xx10^11)/(2pi) =2.39xx10^10Hz`
(b) `B_0=2xx10^-7T, E_0=cB_0=(3xx10^8)xx2xx10^-7=60Vm^-1`
In electromagnetic wave, the electric field is varying sinusoidally with x and t, perpenducular to the
direction of magnetic field as well as the direction the propagation of electromagnetic wave. So electric field
is varying along z-direction. Thus, `E_z=E_0sin ((2pix)/(lambda)+(2pit)/T)=60sin(0.5xx10^3x+1.5xx10^11t)V//m`