Answer to Question #207005 in Electricity and Magnetism for Praneeth

Question

Two linearly polarized waves 4₁(2,0) = 3 cos(kz- wt) and (2,1)= 2 cos(kz-wt + 0) moving along x and y axis respectively is superposed with each other. Draw the path traced by the resultant electric vector for each polarised state for the values of 0 [0,0,0=Tabulate the values of the characteristic parameters of the curves corresponding each polarized state.

Answer 1

The size and phase of each output as a function of the frequency at which the input is sinusoidally stimulated are easily described in linear systems. Because sinusoids of various frequencies may be overlaid to create any arbitrary input waveform5, and the output of a linear system is the superposition of its responses to each superimposed input, this simple classification is adequate. In the same way, systems with many inputs and outputs may be described. Nonlinear systems are more difficult to define since their output frequencies are often harmonics of their input frequencies.

Because free space is a linear system, its response to sinusoidal plane waves properly characterizes it. For example, in Figures 2 and 3, the arbitrary z-propagating x-polarized uniform plane wave might be sinusoidal and represented by

$E (r , t) = xˆE_o cos [k(z − ct)]$

$H (r, t ) = yˆ \sqrt{ε_o /μ_o }E c o os [k(z − ct)]$

The table is shown below