The following is the work of P. Leuchtmann, ETH Zurich.

The Field on the Surface of a Conducting Sphere

We consider a well conducting sphere with diameter  d. The sphere is placed in free space and is illuminated by a linearly polarized plane wave.  Our focus is both on the electric field vector E  and the magnetic field vector  H  on the sphere's surface. In spite of the  structures simplicity we shall find that the full electromagnetic field is amazingly complicated. In case of low frequencies the sphere is simply polarized and the direction of incidence of the illuminating wave is of low importance while for higher frequencies we find a much stronger field on that side where the illuminating wave is coming from and we observe a distinct shadow region on the opposite side.  This is exactly what we would expect for visual light when the diameter  d  is supposed to be considerably larger than the wavelength ë of the electromagnetic wave.
We study two cases: the low [but not too low...] frequency case (with d =ë/3) and the not really high frequency case (with d = 3ë). The first choice shows fields which are clearly different but not too far away from static fields while the second choice is  'not yet the optical case'.
 

The Low Frequency Case

This is the basic picture showing the instantaneous electric field on the surface of the sphere.  The blue arrows represent the electric field vectors at time  t = 0 while the colors show the intensity on a scale starting at light blue [low values] over cyan magenta to yellow [high values]. The arrows represent the values on the exact surface of the sphere. However, for graphical reasons (mainly hiding problems of the graphics routines with other surface elements) they are slightly moved away from the surface.

In the foreground the true sphere with black  x-y-z-coordinate axes (origin in the sphere's center) is shown. The gray grid marks the surface of a `magic mirror' actually located one diameter behind the sphere and mirroring only the field representations but no further geometrical objects such as the coordinate axes or the thick yellow arrow. The latter represents the illuminating wave. It has an oval cross section which allows it to express not only the propagation direction but also the polarization of the incident wave. In our case the excitation is an  x-polarized plane wave propagating upwards into +z-direction. Again: Thanks to the mirror, one can also see the field on the back side of the sphere. This is not particularly interesting in the present case because the absolute value is symmetrical. Only the direction of the field vectors is opposite: the arrows are partly covered by the painting of the surface. 
You may learn more about this field by inspecting an animated version of this picture.  For stressed people with a slow net connection there is a small size version [132 kBytes]. More relaxed people admire the full size version [820 kBytes].

This is the full list of field representations of the same physical structure at the low frequency:
Clicking the number in the size column shows the respective version including some additional remarks.
 

Picture	Size[kBytes]	Description
	820 132	Electric field, time movie in front of mirror
	802 119	Electric field amplitude, rotation movie in front of mirror
	1085 136	Magnetic field, time movie in front of mirror
	570 100	Magnetic field amplitude, rotation movie in front of mirror
	954 122	Direct E-H-amplitude comparison, rotation movie
	428 85	Poynting field (energy flux), time movie
	408 84	Time average Poynting field (energy flux), rotation movie

The High Frequency Case

As compared to the previously discussed low frequency case the only change here concerns the frequency which has been increased by a factor of ten. Before the diameter of the sphere was about one third of a wave length while now we deal with a 3ë-diameter sphere. Some of the effects, e.g., the polarization effect hold while other effects such as the creeping waves become even stronger. As before we treat a number of field representations which may be obtained by selecting the appropriate links in the table below.

All remarks concerning the representation of the fields still hold and need not be repeated. Painting is always on a light blue - cyan - magenta - yellow scale where yellow represents the maximum value.

This is the full list of field representations of the same physical structure at the high frequency:
Clicking the number in the size column shows the respective version including some additional remarks.
 

Picture	Size[kBytes]	Description
	981 139	Electric field, time movie in front of mirror
	454 84	Electric field amplitude, rotation movie
	1157 162	Electric field in E- and H-plane
	879 133	Magnetic field, time movie in front of mirror
	403 79	Magnetic field amplitude, rotation movie
	1339 166	Magnetic field in E- and H-plane
	442 84	Poynting field (energy flux), time movie
	374 78	Time average Poynting field (energy flux), rotation movie
	1241 157	Poynting field (energy flux) in E- and H-plane