G L Pollack and D R Stump Electromagnetism

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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

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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.)

4. Electrostatics with Conductors

G L Pollack and D R Stump Electromagnetism

3

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

where A, B, C, D are constants that will be determined by the boundary conditions. Then the electric field isE = V .

coscos

),(2

rDCr

B

r

ArV

(Section 4.3)