Question

The magnetic field in a plane electromagnetic wave is given by `B_(y) = 2xx10^7 T sin (0.5xx10^3x+1.5xx10^11 t) T`
(a) What is the wavelength and frequency of the wave?
(b) Write an expression for the eletric field.

Answer 1

(a) Wavelength
From the given equation,we can see that
`= k=0.5xx10^3 m^(-1)`
`k=(2pi)/lambda`
`lambda =(2pi)/k=(2pi)/0.5xx10^3`
`=1.25xx10^-2 (m)`
Frequency
Angular frequency,
`omega=1.5xx10^11 rad//s`
But `omega=2pif`
`f=omega/(2pi)=(1.5xx10^11)/(2pi)`
`=2.39xx 10^10 Hz`
(b) `c = E_0/B_0`
`E_0 = cB_0`
`=(3.0xx10^8)(2xx10^7)`
`= 60V//m`
From the relation
`c = Exx B`
We can that `E` is along z-direction.
`:. E_z=(60 V//m)sin(0.5xx10^3x+1.5xx10^11 t) V//m`.