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Monochromatic Plane Wave

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Write the (real) electric and magnetic fields for a monochromatic plane wave of amplitude Eo, frequency w, and phase angle zero that is (a) traveling in the negative x direction and polarized in the z-direction; (b) traveling in the direction from the origin to the point (1,1,1), with polarization parallel to the xz plane. In each case, sketch the wave, and give the explicit cartesian components of k and n.

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Solution: For a monochromatic plane wave of amplitude , frequency , and phase angle zero, polarized in the direction , the electric and magnetic fields are given by
But the physical field is given by the real part of this complex expression. We know that the real part of is .
There fore the actual electric and magnetic fields for a monochromatic plane wave becomes

(a) Consider a ...

Solution Summary

The solution solves for and writes the monochromatic plane wave specified. The polarization parallel to the xz planes are determined. The expert sketches the waves for explicit cartesian components.

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Wave solutions of Maxwell's equations and Ampere-Maxwell law

An electromagnetic signal is generated by a Hertzian dipole located at a point P, which has the position vector r = ?(100m) ez. The signal is detected by a small wire loop located at the origin. Apart from the dipole and the loop, the nearby space is empty.

Experimentation reveals that the detected signal is induced by a changing magnetic field:
Bphys(t)= B0 sin (2?ft) ex, where B0 =0.1 ?T and f = 30MHz.

Show that the given physical magnetic field at the loop, Bphys(t), is consistent with a monochromatic plane wave solution of Maxwell's equations given by B =iB0 exp[i(kz ? ?t)] ex.

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