The magnetic field in a plane electromagnetic wave give by `B_(y)=(2xx10^(-7))T sin (0.5xx10^(3)x+1.5xx10^(11)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`B_(y)=B_(0)sin[2pi[((x)/(lambda)+(t)/(T))]`
we get `lambda=(2pi)/(0.5xx10^(3))m = 1.26cm` and `(1)/(T)=v=(1.5xx10^(11)//2pi)=23.9 GHz`
(b) `E_(0) = B_(0)c = 2xx10^(-7) -7 T xx 3 xx 10^(8) m //s = 6 xx 10^(1) 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(0.5xx 10^(3) xx +1.5xx10^(11) t)V//m`