The oscillating magnetic field in a plane electromagnetic wave is given by
`B_(y)=(8xx10^(-6))sin [2xx10^(11)t+300 pi x ] T`
(i) Calculate the wavelength of the electromagnetic wave.
(ii) Write down the expression for the oscillating electric field.

Explanation

Given equation is `B_(y)=(8xx10^(-6))sin [2xx10^(11)t+300 pi x]T`
Comparing the given equation with the equation of magnetic field varying sinusoidally with x and t
`B_(y)=B_(0)sin ((2pi x)/(lambda)+(2pi t)/(T))`
We get, `(2 pi)/(lambda)=300 pi :. lambda=(2)/(300)=0.0067 m. and B_(0)=8xx10^(-6)T`
(i) Wavelength of the electromagnetic wave `lambda=0.0067m ` or 0.67 cm
(ii)`E_(0)=CB_(0)=3xx10^(8)xx8xx10^(-6)=24xx10^(2)=2400 Vm^(-1)`
`:.` The required expression for the oscillating electric field is
`E_(z)=E_(0) sin ((2 pi x)/(lambda)+(2pi t)/(T))=2400 sin (300 pi x + 2 xx 10^(11)t)` v/m.