PHY294H - Lecture 4

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 $p \approx e \times 10^{-10}m$.

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 $E = \sigma/\epsilon_0$.

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.

Shell theorems

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.

Demonstrations

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.