EXAM 1 March 8, 1988 PS 208
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 -7
1/(4 pi epsilon ) = 9.0 x 10 N m / C mu /(4 pi) = 10 T m / A
0 0
-31
The mass of the electron is 9.11 x 10 kg.
1. (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. [8 points each part]
[The remaining problems count 28 points each.]
2. In the Bohr model of the hydrogen atom, an electron
circles a proton at a radius of a . How fast must the electron
0
be moving if no forces other than the Coulomb attraction are large
enough to matter?
3. (From homework) A thin cylindrical shell of radius R is
1
surrounded by a second concentric concentric cylindrical shell of
radius R . The inner shell has a total charge +Q and the outer
2
shell -Q. (a) Assuming the length L of the shells is much
greater than R or R , determine the electric field as a function
1 2
of r , the perpendicular distance from the common axis of the
cylinders (the usual cylindrical-coordinate r) everywhere (i. e.
inside both cylinders, between the two, and outside both).
4. A rod of length L is placed a distance b to the right of the
origin. The charge density (Coul/m) on the rod is
2 2 3/2
lambda = -c ( x + a )
What is the electric field at the point x=0,y=a ? Note that a
occurs in two different places in this problem.