Suppose that the electric field part of an electromagnetic wave in vacuum is
` vecE = ((3.1 N//C cos [(1.8 rad // m ) y + ( 5.4 xx 10 ^6 rad s^(-1) t ) ]} hati `
(a) What is the direction of propagation ?
(b ) what is the wavelength ` lamda `?
(c ) what is the frequency v?
(d) what is the amplitude of the magnetic field part of the wave ?
(e ) write an expression for the maganetic field part of the wave .

Explanation

(a) from the expression of electric of electric field , the direction of propagation of the wave Is along negative Y - direction , i.e., along - `hatj`
(b ) comparing the given equation with the standard equation
` E=E_0 cos ( ky + omega t ) , ` we get
` k-=1.8 rad //m , omega = 5.4 xx 10 ^6 ` rad /s
`E_0 = 3.1 N//C `
Wavelength `, lamda = ( 2pi )/( k ) = ( 2 xx 3.14 )/( 1.8 ) = 3.48 m`
` ~~ 3.5 m`
(c ) Frequency , `v = ( c ) /( lamda ) =( 3 xx 10^8 ) /( 3.5 )`
` ~~ 85.7 xx 10^6 Hz ~= 86 MHz`
(d) amplitude of magneatic field is
` B_0 = (E_0 )/(C ) = ( 3.1 )/( 3 xx 10^8 )`
` = 1.03 xx 10^(-8 ) T = 10.3 nT `
(e ) `B = B-0 cos ( ky + omega t )`
` therefore vecB = ( 10. 3 nT ) cos [(1.8 rad //m ) y + ( 5.4 xx 10^6 rad //s t] hatk `