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 `vec(B)=(1)/(c)hat(k) xx vec(E)=(1)/(omega)(vec(k)xxvec(E))`
B. The electromagnetic field can be written in terms of the associated magnetic field as `vec(E)=c(vec(B)xxhat(j))`
C. `hat(k).vec(E)=0,hat(k).vec(B)ne0`
D. `hat(k).vec(E)=0,hat(k)xxvec(B)=0`

Answer

A

Explanation

We know that, direction of propagation of electromagnetic wave is always along the direction of vector product `(vecExxvecB)`
`vecB=Bhatj=B(hatkxxhati)=(E)/(c)(hatkxxhati)rArrvecB=(1)/(c)[hatkxxEhati]=(1)/(c)[hatkxxvecE]`
If write the equation in terms of magnetic field, then
`vecE=c(vecBxxveck)`.
`hatk.vecE=hatk.(Ehati)=0, hatk.hatB=hatk.(Bhatj)=0,`
as angle between them is `90^(@)`.