Recommended work to prepare for lecture 5
Read: FGT Chap. 24
Do concept questions: 1-14
What's in a field?
Does it bother you to think that there are
mysterious fields that are everywhere around
us? What carries these fields? What exactly
are they? We have a very clean operational
definition of the electric field at a point
in space, but how exactly does a point
charge influence another point charge that
is physically separated from it? The way in which
we understand this is based on quantum physics.
Each force has particles which are the ``carriers''
of the force. In the case of EM, the carrier
is the photon. A charge is seen as
producing virtual photons which then
may interact with a second point charge placed
in this photon field. The concept
of electric field lines is a very
nice conceptual tool, which captures the
physics without having to deal with
the photon field which actually carries
the electric force from one
charge to another.
Permanent and Induced dipoles
Molecules like water have a permanent dipole moment due to the charge separation that occurs during bonding. In the case of water the oxygen is more negative than the Hydrogen atoms. An estimate of the permanent dipole moment of water is .
Other atoms, like Xenon, do not have a permanent
dipole moment as their electron configuration
is perfectly symmetric. Nevertheless an
electric field can induce a dipole moment.
Since the size of the dipole moment increases
with the linear dimension of the dipole, larger
objects have the potential for larger induced dipoles.
Micron-sized grains can have large induced dipoles
which want to align with the electric field in the
same way that permanent dipole moments do. Induced
dipoles are very important even at the atomic scale,
for example they are the atomic origin of dispersion
forces. At the atomic scale there is the
possibility of: permanent dipole-permanent dipole;
permanent dipole - induced dipole and; induced dipole-induced dipole
forces. All of these forces fall off as 1/r6 and
are often lumped together into a single Van der Waals
interaction. You might notice that the terminology in
textbooks is inconsistent in the definition of what
a Van der Waals interaction is. For example, some books
treat the permanent dipole-permanent dipole
force as a separate force which is not included
in the Van der Waals interaction.
Dipole in a non-uniform field
A dipole in a uniform field has no center of mass
acceleration as there is no net force on the center
of mass of the dipole. However if the dipole is
placed in a non-uniform field, the dipole aligns
with the direction of the non-uniform field
and moves toward regions of higher electric field.
This is what happens in the attraction of paper to
a comb and the bending of a stream of water
by a charged rod. The dipole may be an induced dipole, as
in the case of paper or there may be a permanent
dipole, as is the case of water.
The strange case of conductors
Conductors have the following properties:
1. If there is no current flowing, the electric field inside a conductor is zero.
2. If there is no current flowing, the electric field is normal to the surface of the conductor. Just outside the surface we have .
3. If there is no current flowing, excess charges always
lie on the surface of a conductor. Actually the excess
charges arrange themselves on the surface in order
to make the electric field inside the conductor zero.
Note that these theorems apply to both conductors and insulators.
1. The electric field inside a uniform shell of charge is zero.
2. The electric field outside a uniform shell of charge is like
that of a point charge located at the center of the shell.
A conducting spherical shell
A case of particular importance is a conducting spherical
shell. When a free charge Q is place on a conducting
spherical shell, the charge goes to the outer surface
of the shell. The shell theorem ensures that
the electric field inside the conductor is
zero, even though there is no charge
on the inner surface of the spherical shell. This
enables a conducting spherical shell to
be ``pumped'' to a high charge level, by
repeatedly adding a small amount of charge to the
inner surface of the shell. This is the
principal of operation of the Van de Graff generator.
1. Charges produced by bringing materials
together, and/or by friction.
2. Deflecting a stream of water.
3. Charging by induction.
4. Electric field lines.
5. Wimshurst machine.