Introductory Physics Volume Two

44 Electric Potential 2.4
Theorem: Conductor in Equilibrium: Potential
All points in a conductor at equilibrium have the same electric
potential.
Theorem: Conductor in Equilibrium: Surface Field
The field at the outside surface of a conductor in equilibrium is
normal to the surface of the conductor. The magnitude of the
field is E = σ ɛ 0
where σ is the surface charge density.
We can see that the previous theorem must be true by considering
that the surface of the conductor is an equipotential, and noting that
the electric field is normal to any equipotential surface.
⊲ Problem 2.6
There is a solid conductor with a cavity within it. Floating within this
cavity there is a second conductor. This has been drawn below with a
quarter of the outer conductor removed so that you can see the inner
conductor.
A total charge Q a is place on the inner conductor and a charge Q b is
placed on the outer conductor.
(a) What is the amount of charge on the inside surface of the outer
conductor?
(b) What is the amount of charge on the outer surface of the outer
conductor?
⊲ Problem 2.7
A conducting spherical shell having an inner radius of 4.0 cm and outer
radius of 5.0 cm carries a net charge of +10µC. If a +2.0µC point charge
is placed a the center of this shell, determine the surface charge density
on the inner and outer surfaces.