EXAM 1 March 6, 1996 PS 208
YOUR NAME:________________________________________________
If you need a constant not given here or do not understand a
problem, please ask me about it. No notes, books, etc. may be used
during this exam.
2 -19
g = 9.8 m/sec e = 1.6 x 10 C
9 2 2
1 / (4 pi epsilon )= 9.0 x 10 N m / C
0
-31
The mass of the electron is 9.11 x 10 kg.
1. [10 points]
(a). Describe a good way to reconstruct Coulomb's Law
without memorization. You need not have a technique for finding
the arbitrary form of the constant, and you may use anything
in the heading of this exam.
(b). Explain a good technique for determining
without memorization how to determine the constant in Gauss's
Law. You may assume that you know Coulomb's Law.
For the remaining problems, place the equations representing the
physics principles you are using in the box on the page. You may
use and English label for the principle, the general form of the
equation, or the form you get applying the principle to the problem
at hand. Each question counts 30 points.
2. Two point charges Q and Q are a distance d apart,
1 2
and their combined charge is Q . If they repel each other
tot
with a force F, find the two charges in terms of Q , d , and F.
tot
Diagram, if any:
Principles:
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3.
(a) What is the potential difference between two cylinders
each of length L, when there is a charge +Q on the outer
cylinder and -Q on the inner. The radii of the inside and outside
cylinders are R and R respectively.
1 2
Diagram:
Principles:
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4 (From homework). A solid nonconducting sphere of radius
r has a total charge Q which is distributed according
0
to rho = br , where rho is the charge per
unit volume (charge density) and b is a constant. Determine
the electric field at all points inside the sphere. Notice
that rho cannot be taken out of radial integrations,
but is a constant with respect to angular integrations. [If
you have trouble with dV, write out the closest form you can
and box it so I will know what you are using.]
Diagram:
Principles:
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Use this page to continue # 4.