An electromagnetic wave travelling in the X- direction has freqency of `2 xx 10^(14)` Hz and electric field for this wave ?

Options

A. `vecB ( x,t) = ( 3 xx 10^(-8) T ) sin [ 2pi ( 1.5 xx 10^(-6) x -2 xx 10 ^4 t)]`
B. ` vecB ( x, t) = ( 9 xx 10 ^(-8) T hatk sin [ 2 pi ( 1.5 xx 10^(-6 ) x-2xx 10^4 t ) ]`
C. ` vecB ( x, t) = ( 9 xx 10^(-8) T )hati sin [ 2 pi ( 1.5 xx 10^(-6) x - 2 xx 10^4 t)]`
D. `vecE (X,t) = ( 9 xx 10^(-8) T ) hatj sin [ ( 1.5 xx 10^(-6) x -2 xx 10^4 t)]`

Answer

B

Explanation

The relation between the amplitudes of the electric field and the magnetic is given by
` B_0 = (E_0 )/(c ) `
thus , `B_0 = (27)/( 3xx 10^8 ) = 9 xx 10^(-8) T `
the angular frequency is given by
`omega = 2pi f = 2 pi xx 2xx 10^(14) Hz `
The direction of oscillation of the magnetic field can be either along Y - axis or z- axis
thus the possible choice should be
` vecB (x,t) = ( 9xx 10 ^(-8) T ) hatk sin `
` [ 2 pi ( 1.5 xx 10^(-6) x-2 xx 10^(14) t)]`
HEnce the correct option is (b)