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

Explanation

The given equation `E_(y) = 0.5 cos[2pi x10^(8)(t – x//c)]` ..... (1)
indicates that the electromagnetic waves are propagating along the positive direction of X-axis.
(b) The standard equation of electromagnetic wave is given by
`E_(y) = E_(0) cos omega(t – x//c)` . .... (2)
Comparing the given eq. (1) with the standard eq. (2), we get
`omega = 2pi xx10^(8)`
or ` 2piv = 2pi xx10^(8)`
`therefore v = 10^(8)` per second
Now,` lambda = c/v = (3xx10^(8))/10^(8)=3`m
(c) Here, the wave is propagating along X-axis and electric field is along Y-axis and hence the magnetic field must be along Z-axis. So the components of associated magnetic field are :
`B_(x) = 0, B_(y) = 0`
and `B_(z) =B_(0) cos [2pixx10^(8)(1-x/c)]`
`B_(z) =E_(0)/c cos [2pixx10^(8)(1-x/c)]`
`B_(z) =(0.5)/(3xx10^(8)) cos [2pixx10^(8)(1-x/c)]`