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.

Solution Summary

We solve a problem in electromagnetism involving a Hertzian dipole.

The question attached is from this page.
http://farside.ph.utexas.edu/teaching/em/lectures/node48.html
Please answer with vector notation. The question is only about (450) so I don't believe that you have to read through all of it to answer.

2. (a) (i) Write down Maxwell'sequations for static electric and magnetic ﬁelds in the vacuum (note that you should include charge and current densities).
(ii) How did Maxwell modify Ampére's law to account for dynamic electric ﬁelds?
(b) In a region of space in which the relative permittivity is (attached equation),

1. What is the definition of displacement current and how does it arise? Does displacement current have any real significance? Explain
2. Write down the maxwell'sequations of electromagnetism, and state the laws they represent. Explain the meaning of all the symbols used.

Derive Maxwell's Relations from First and Second Laws of Thermodynamics and Thermodynamic Functions like Internal Energy, Helmholtz's Function, Enthalpy and Gibbs Free Energy.
And also explain how they are satisfied by an ideal monatomic gas?

Tom's rocket ship is moving away from Kathy at 0.75c. He fires a laser beam in the backward direction, toward Kathy. According to Galilean relativity. How fast does the laser beam move relative to Kathy, assuming that Tom observes the beam to move away from him at speed c? How fast according to Einstein's relativity? Why?

The equation for a wave moving along a straight wire is: (1) y= 0.5 sin (6 x - 4t)
To look at the motion of the crest, let y = ym= 0.5 m, thus obtaining an equation with only two variables, namely x and t.
a. For y= 0.5, solve for x to get (2) x(t) then take a (partial) derivative of x(t) to get the rate of change of

The magnetic susceptibility per unit volume of a magnetic solid is given by x = A/(T-theta) where A and theta are constants independent of magnetic field. How much does the entropy per unit volume of this solid change if, at the temperature T, the magnetic field is increased from H = 0 to H = H_o?