Wow. We certainly have a range of answers on this one. And I believe most
of them are wrong. I believe Joseph Bellina and Bill Beaty have it correct.
If charges are outside a conductive hollow sphere, there will not be any
electric field inside the sphere due to those charges regardless of whether
the sphere is grounded or floating.
If there are charges inside the sphere cavity, whether these cause electric
fields outside the sphere does depend on whether the sphere is grounded or
not. If the sphere is not grounded there is electric field outside. If the
sphere is grounded there is no electric field outside.
Take the simple case of single positive charge at the center of a conductive
spherical shell. Let's do the ungrounded sphere first. Draw a spherical
Gaussian surface outside the conductive shell. Is there net charge inside
this Gaussian surface? Yes. Why? There is a positive charge at the center
of the spherical shell; we put it there. The spherical shell, although
polarized, has no net charge. Therefore the net charge inside the Gaussian
surface is the single charge we put at the center. Therefore, there must be
electric flux through this Gaussian surface (which is outside the sphere).
Now ground the sphere. Negative charge from the earth goes to the inner
surface of the conductive shell. Now return to our Gaussian sphere outside
the conductor. Now there is zero net charge inside it. The positive charge
at the center is still there, but equal negative charge has migrated to the
inner surface of the conductive shell from the earth, so the net charge
inside the Gaussian surface is zero. There is no electric flux through the
Gaussian surface. In general, zero electric flux through a closed Gaussian
surface does not guarantee there is zero electric field at every spot on
that Gaussian surface, but it does guarantee just that in this symmetric
case.
I used a symmetric and static example. What happens if the charges inside
are not symmetrically distributed and are moving around? Basically the same
result as long as they are moving slowly enough that the charges from the
earth have time to distribute themselves on the inner surface of the shell
into the proper arrangement to keep the electric fields in the metal of the
conductive shell at zero.
Another way to view this... as long as things don't move too fast, the
electric field inside the metal of the conductive shell remains zero. In
the grounded situation all charges and charge movements are happening inside
the cavity or on the inner surface of the shell. In the non-grounded case
there is also charge and possibly charge movement on the outer surface
because the shell gets polarized and these outer guys are the "mates" of the
charges that went to the inner surface. In the grounded case these "mates"
are in the earth.
I got involved in a lot of shielding problems when I was designing nuclear
detectors and using them around accelerators, etc. Most things were
solvable as long as we didn't get into too high of frequencies.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817