Given the electric field of a 200 MHz uniform plane wave propagating in the z^ d

Question

Given the electric field of a 200 MHz uniform plane wave propagating in the z^ direction, where E is parallel to the y axis and reaches a peak value of 150 (mV/m) at t = 0 (s) and z = 0.5 (m).

(a) Write the expression for the electric field of the wave in free space.

(b) Write the expression for the electric field of the wave in polystyrene (µr = 1, er = 2.53).

I sorta understand part a. The problem is our professor hasn't given us an example of writing a wave equation in a medium (polystyrene).

Explanation / Answer

f = 200 MHz, uniform plane wave propagating in the z^ direction, where E is parallel to the y axis and reaches a peak value of Emax = 150 (mV/m), at t = 0 (s) and z = 0.5 (m).

(a) Write the expression for the electric field of the wave in free space. speed v = c = 3.00*108 m/s, = v/f E = Emax cos[2ft - 2/ (z - 0.5)] = Emax cos[2(ft - fz/v + 0.5f/v)] E = 150 cos[2(108 t - 0.667 z + 0.333)] (b) Write the expression for the electric field of the wave in polystyrene (µr = 1, r = 2.53). v = c/(r*r) = 1.886*108 m/s E = Emax cos[2(ft - fz/v + 0.5f/v)] E = 150 cos[2(108 t - 1.060 z + 0.530)]

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