PHYS-222 Worksheet 5 for Section 25 & 36
TA: Yang Li, leeyoung@iastate.edu
September 16, 2012
Problem 5-1
(a) A conducting sphere with radius a has charge q. Draw the potential V (r) and the magnitude of electric
field E(r) as functions of r (including r < a region).
(b) If conducting sphere is hollow, will the answers change of not? Why or why not?
(c) A solid sphere wit radius a has uniformly distributed charge q. Draw the potential V (r) and the
magnitude of electric field E(r) as functions of r (including r < a region)
Problem 5-2
A conducting hollow sphere can be viewed as a capacitor with respect to the ground. The electric potential
of the ground is about 0V . Suppose the radius of the sphere is a.
(a) If given charge Q on the sphere, what is its potential V ? (V =
q
4πε0 a )
(b) What is its capacitance C ? (C = 4πε0 a)
(c*) In reality, this capacitor is easity influenced by the environment. This can be fixed by adding a
cooriginal hollow sphere outside the first one. Suppose the radius of the second sphere is b. What is
the capacitance C of this capacitor? Suppose d = b − a, d a. Express your answer in terms of the
area of the capacitor A, and the separation distance d. Compare your result with the parallel-plate
capacitor. (C = ε0dA 1+1 d roughly the same as parallel-plate capacitor. When a d, it can be viewed
a
as a parallel-plate capacitor, with overall curvature.)
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