Electric field of an electromagnetic wave is , `E=10^(-5)` sin `(12xx10^15 t - 4xx10^(7)x)`.Find the frequency , velocity , wavelength of the wave . Write the equation of the magnetic field corresponding to this wave. Assume all quantities in SI unit.

Explanation

Electric field of the given electromagnetic wave,
`E=10^(-5) "sin"(12xx10^15 t-4xx10^7 x)`
Comparing with the expression for electric field,
`E=E_0 "sin"(omegat-kx)` we get,
`omega =12xx10^15 "rad".s^(-1)`
`therefore 2pif=12xx10^15`
or , `f=(12xx10^15)/(2pi)=1.9xx10^15` Hz.
Hence, frequency of wave, `f=1.9xx10^15` Hz
Velocity of wave,
`v=omega/k=(12xx10^15)/(4xx10^7)=3xx10^8 m.s^(-1)`
Wavelength , `lambda=c/f =(3xx10^8)/(1.9xx10^15)=1.58xx10^(-7)` m
Equation of the corresponding magnetic field,
`B=B_0 "sin" (omegat-kx)=E_0/c "sin" (omegat -kx) [ because E_0/B_0=c]`
`=10^(-5)/(3xx10^8)"sin"(12xx10^5t-4xx10^7 x)`
`=3.33xx10^(-14) "sin" (12xx10^15t-4xx10^7 x) T`