A charged particle oscillates about its mean equilibrium position with a frerquency of `10^9 Hz`. The electromagnetic waves produced by the oscillator?

Explanation

Electric field amplitude of `E_(0)=120N//C`
Frequency of source, `v=50.0MHz=50xx10^(6)Hz`
Speed of light, c=3`xx10^(8)m//s`
(a) Magnitude of magnetic field strength is given as:
`B_(0)=(E_(0))/(c)`
`=(120)/(3xx10^(8))`
`=4xx10^(-7)T=400nT`
Angualr frequency of source is given as:
`omega=2nv`
`=2nxx50xx10^(6)`
`=3.14xx10^(8)` rad/s
Propagation constant is given as:
`k=(omega)/(c)`
`=(3.14xx10^(8))/(3xx10^(8))=1.05` rad/m
Wavelength of wave is given as:
`gamma=(c)/(v)`
`=(3xx10^(8))/(50xx10^(6))=6.0m`
(b) Suppose the wave is propagating in the positive x direction. then, the electric field vector will be in teh positive y direction and the magnetic field vector wil be in the positve z direction . This is because will three vectors are mutually perpendicular.
Equation of electric field vector is given as:
`vecE=E_(0)sin (kx-omegat)hatj`
`=120sin[1.05x-3.14xx10^(8)t]hatj`
and, magnetic field vector is given as:
`vecB=B_(0)sin(kx-omegat)hatk`
`vecB=(4xx10^(-7))sin[1.06x-3.14xx10^(8)t]hatk`