Question

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 eletric field.

Answer 1

(a) Comparing the given equation with
`B_(y)=B_(0)sin[2pi((x)/(y)+(t)/(T))]`
We get `lamda=(2pi)/(0.5xx10^(3))m=1.26cm`, and `(1)/(T)=v=(1.5xx10^(11))//2pi=23.9GHz`
(b) `E_(0)=B_(0)c=2xx10^(-7)Txx3xx10^(8) m//s =60 V// m`
The electric field component is perpendicular to the direction of propagation and the direction of magnetic field. Therefore the electric field component along the z-axis is obtained as
`E_(z)=60sin(0.5xx10^(3)x+1.5xx10^(11)t) V//m`