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 `vecB=1/c hatkxxvecE`
B. The e.m. wave field can be written in terms of the associated magnetic field as `vecE=c(vecBxxxxhatk)`
C. `hatk.vecE=0, hatk.vecB=0`
D. `hatkxxvecE=0, hatkxxvecB=0`

Answer

(a,b,c)

Explanation

Suppose an em wave is travelling along negative z-direction. Its electric field is given by
`vecE=vecE_0cos (kz-omegat)`
which is perpendicular to z-axis. It acts along negative y-direction.
The associated magnetic field `vecB` in em wave is along x-axis, i.e., along `hatkxxvecE`.
As `B_0=(E_0)/c :. vecB=1/c(hatkxxvecE)`
Thus, option (a) is correct.
The associated electric field can be written in terms of magnetic field as `vecE=c(vecBxxhatk)`
Thus, option (b) is correct.
Angle between `hatk and vecE` is `90^@`. Therefore, `hatk. vecE=1Ecos 90^@=0`
and `hatk.vecB=1vecEcos 90^@=0.` Thus, option (c) is correct.