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The electric field of a plane electromag...

The electric field of a plane electromagnetic wave in vacuum is represented by `vecE_x=0`, `vecE_y=0.5 cos[2pixx10^8(t-x/c)], vecE_z=0`
(a) What is the direction of propagation of electromagnetic wave?
(b) Determine the wavelength of the wave.
(c) Compute the component of associated magnetic field.

Text Solution

Verified by Experts

(a) Equation `vecE_y` shows that the electromagnetic
wave travels along hte positive x-axis.
(b) Wave length of wave,
`lambda=c/v=c/((omega//2pi))=(2pic)/omega=(2pixx(3xx10^8))/((2pixx10^8))=3.0 m`
(c) Since the magnetic field vector is perpendic-
ular to the electric field vectors as well as to the directions of propagation of electromagnetic wave,
so magnetic field must be varying along z-axis.
Therefore,
`vecB_x=0,vecB_y=0` and
`vecB_z=0.5/(3xx10^8) cos [2pixx10^8(1-x/c)]`
`[:' B_0=(E_0)/c]`
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