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 hatk xx vecE = 1/omega ( hatk xx vevE)`.
B. The electromagentic field can be written in terms of the associated magnetic field as ` vecE = c ( vecB xx hatk).`
C. ` hatk . vecE = 0, hatk vecB =0`
D. `hatk xx vecE =0, hatk xx vecB =0`

Answer

A, B, C

Explanation

Let us consider an electromagnetic wave is travelling along Z-direction. The electric field vector is given by
` vecE = E_0 cos ( kz - omega t) ` (j )
It acts along the Y- direction. So, the associated magnetic field is along the X axis, i.e. along `hatk xx vecE `
`therefore vecB = ( hatk xx E )/(c ) a s vecB = vecE //c `
Also, the associated electric field can be written in terms of magnetic field as
` vecE = c ( vecB xx hatk )`
The angle between ` hatk ` and `vecE`is `90^@`. So, `hatk . E=0.` Also, the angle between k and B is `90^@`. Thus, k-B is also equal to zero.
The correct options are (a), (b) and (c).