Transcript Chapter 4. Electrostatics and Conductors

4. Electrostatics with Conductors
General statements about E(x) in or near a conductor
• E is 0 inside the conducting material.
• E is normal at the surface.
• The surface charge density is  = 0En .
• The conductor is an equipotential.
(Explain why each statement must be true.)
G L Pollack and D R Stump
Electromagnetism
1
4. Electrostatics with Conductors
The Method of Images
• The image of a charge q in a planar conducting surface
is a charge q = – q located at an equal distance on the
opposite side of the surface.
• The image of a charge q in a conducting sphere of
radius a is a charge q= – qa/r located at the conjugate
point, i.e., at radius r = a2/r.
(Explain why the image charge is not real but a useful fiction.)
G L Pollack and D R Stump
Electromagnetism
2
4. Electrostatics with Conductors
In some simple, azimuthally symmetric problems
involving a spherical conducting boundary, the potential in
a charge-free region takes the form
A B cos
V ( r , )  
 C  D r cos
2
r
r
where A, B, C, D are constants that will be determined by
the boundary conditions. Then the electric field is
E = V .
(Section 4.3)
G L Pollack and D R Stump
Electromagnetism
3