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

Explanation

Given,
`B_(y)=2xx10^(-7)sin[0.5xx10^(3)xx+1.5xx10^(11)t]T`
Comparing with proved equation,
`B_(y)=B_(0)sin[kx+omegat]`
Here, `B_(0)=2xx10^(-7)T,k=0.5xx10^(3)rad//m`
and `omega=1.5xx10^(11)rad//s`
Now, `(E_(0))/(B_(0))=c" "` [ c is velocity of light ]
`E_(0)=(3xx10^(8))xx(2xx10^(-7))`
`E_(0)=60N//C`
(b) Now, `omega=1.5xx10^(11)rad//s`
`implies2piv=1.5xx10^(11)` [ v is frequency ]
`impliesv=(1.5xx10^(11))/(2xx3.14)`
Frequency of the wave,
`v=2.39xx10^(10)Hz`
`:.` As , we know propagation vector
i.e., `k=(2pi)/(lamda)`
`0.5xx10^(3)=(2pi)/(lamda)implieslamda=(0.5xx10^(3))/(2xx3.14)`
Wavelength of the wave, `lamda=79.62`m