We are now in a position which will allow us, at least qualitatively, to describe the origins of electromagnetic radiation and its interaction with atoms and molecules. The description given here largely follows that given by Blatt.

We already know what the dipole field looks like. If we were to measure the field at the point P, a long distance away from the dipole, we would find the field pointing in the negative z direction.

Figure 1. The electric field at t=0.

Let this first measurement be made at time t=0. If the charges execute simple harmonic motion and become inverted at a time t = T/2 and we measure the field at P again the field has the same magnitude but now points in the positive y direction. We would therefore guess that E would vary sinusoidally at P.

The question is, does this sinusoidal variation in E occur at the same instant as the sinusoidal variation in the atomic positions? Maxwell found that in fact the variation in E takes time to propagate through space. The speed at which it does this is given by

( 1),

which is the speed of light, normally denoted c. So changes in the field propagate at the speed of light! We will use this fact to sketch the electric and magnetic field variations for our dipole oscillator.

We imagine that we have stopped the oscillation after one half cycle, i.e. at t = T/2, and measure the electric field pattern at t = T. At a distance r < cT/2 and a distance r > cT the field lines are strictly dipolar, but with the field directions inverted. In the portion of space in between cT/2 and cT the field lines can be determined by remembering that in a region which is free of charges the lines must either be continuous or extend to infinity. The only way to accomplish this is in the way shown below.

Figure 2. The electric field after half a period of dipole oscillation.

Hence if we allow the dipole to execute simple harmonic motion the electric field variation at P would correspond to

E = E0sin(kx - ωt) ( 2),

where E0 is the amplitude at t=0 at position P, and in this case points in the z - direction, ω is the oscillation frequency of the dipole and k is called the wave number and is given by

( 3),

where λ is the wavelength of the undulations in the electric field.

The moving dipole charges of course also constitute a source of magnetic field. Here the direction of motion of the positive charge and negative charge are in opposite direction, but since the sign of the charges is opposite the current produced will point in the same direction.

Figure 3. The magnetic field from the oscillating dipole is equivalent to the field from a straight conductor.

By the right hand rule, it is clear that the magnetic field lines at the point P are perpendicular to the electric field at all times, i.e. they lie in the x-y plane and point in the y-direction. We cannot take our simplified picture of the electromagnetic wave too far at this point. It would predict that the magnetic and electric field were out of phase, whereas they are actually in phase. This error is due to the fact that we have only learned how to determine the magnetic field which is static, when it varies an added complication occurs. The complete theory predicts that the resultant electromagnetic wave at P travels in the x direction and has transverse oscillations in the z direction of the electric field and in the y direction of the magnetic field and that these are in phase.

( 4).

Figure 4. The electromagnetic wave. E oscillates in the z direction B in the y direction. (For code see "Physical Chemistry: Molecular Interactions: Electromagnetic Wave.)

From what we have already seen about the torque created by electric and magnetic fields on dipoles, we would expect that the electromagnetic wave would cause molecules to rotate and precess. Additionally an electrostatic dipole lined up along the z direction in our example would be forced to oscillate. These effects are remarkable, because the conservation of energy tells us that we can transfer vibrational energy across empty space in the form of electromagnetic waves, and thereby induce other dipoles to oscillate or to rotate.