An electromagnetic wave travelling along z-axis is given as `E=E_(0) " cos "(kz- omegat).` Choose the correct options from the following

Options

A. The associated magnetic field is given as `B =1/c hatk xx E =1/omega (hatk xx E)`
B. The electromagnetic field can be written in terms of the associated magnetic field as `E= c(B x hatk)`
C. `hatk .E=0,hatk. B =0`
D. `hatk xx E =0, hatk xx B =0`

Answer

A, B, C

Explanation

Suppose an eletromagnetic wave is travelling along negative z-direction . Its electric field is given by
`E=E_(0) " cos " (kz -omegat)`
Which is perpendicular to z-axis . It acts along negative y-direction.
The associated magnetic field B in electromagnetic wave is along x-axis i.e., along `hatk xx E.`
`"As "" "B_(0) =(E_(0))/(C)`
`:. " " B=1/C (hatk xx E)`
The associated electric field can be written in terms of magnetic field as
`E=c(Bxx hatk)`
Angle between `hatk` and E is `90^(@)` between `hatk` and B is `90^(@)` . Therefore `E =1E " cos " 90^(@) =0` and `hatk . B =1 E "cos " 90^(@) =0`