Suppose that the electric field of an electromagnetic wave in vacuum is `E={(3.0 N //C) cos [1.8 rad//m) y +(5.4 xx 10^6 rad // s)t]}hat i`
(a) What is the direction of propagation of wave?
(b) What is the wavelength lambda ?
(c) What is the frequency `f` ?
(d) What is the amplitude of the magnetic field of the wave
(e) write an expression for the magnetic field of the wave.

Explanation

(a) From the knowledge of wave we can see that electromagnetic wave is travelling along negative y- direction, as `omega t`
and ky both are positive.
(b) `k=1.8 rad//m`
`k = (2pi)/(lambda)`
`lambda = (2pi)/k=(2pi)/1.8=3.5 m`
(c) `omega =5.4xx10^6 rads//s`
`omega=2pif`
`f = omega/(2pi)=(5.4xx10^6)/(2pi)`
`8.6xx10^5 Hz`
(d) `E_0=3.0 N//C`
From the relation,
`c = (E_0)/(B_0)`
We have,
`B_0=(E_0)/c=3.0/(3.0xx 10^8)`
`=10^8 T`
(e) `E` is along hati direction, wave is travelling along negative y-direction. Therefore, oscillations of `B` are along z- direction or
`B = (10^-8 T) cos [(1.8 rad//m)y + (5.4 xx 10^6 rad//s)t ] hat k`.