Suppose that the electric field amplitude of an electromagnetic wave us `E_0=120 N// C` and that its frequency is `50.0 MHz`.
(a) Determine` B_0,omega,k` and `lambda`,
(b) find expressions for `E` and `B`.

Explanation

Given , electric field amplitude `, E_0 = 120 MC^(-1)`
Frequency `, V= 50 .0 MHz = 50 xx 10 ^6 Hz`
(a) Magnetic field amplitude `, B_0 =(E_0 )/(C )= (120) /( 3xx 10^8)`
`= 40 xx 10^(-8) t= 400 nT `
Angular frequency `omega = 2pi v = 2 xx 3.14 xx 50 xx 10 ^6 `
`= 3.14 xx 10 ^8 rad s^(-1)`
wavelength `lamda = (c)/(v ) = ( 3xx 10^8 )/( 50xx 10^6 ) = 6.00 m`
and ` k = ( 2pi )/( lamda) = ( 2 xx 3.142 ) /( 6 ) `
`= 1.05 rad m^(-1)`
(b) since ` vecE = E_0 sin ( kx - omega t ) hatj`
` implies vecE = ( 120 N//C ) sin {[ 1.05 rad //m ] x- { 3.14 xx 10 ^(8) rad //s t] hatj `
and ` vecB = B_0 sin [ Kx - omega t] hatk `
` = ( 4 xx 10^(-7) T ) sin [{ 1.05 rad //m ] x`
` - { 3.14 xx 10^8 rad //s ] t ] hatk `