EXAM 3 March 7, 1990 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. (10 points) 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.
(The remaining problems count 30 points each.)
2. (From homework) A very long solid nonconducting cylinder
of radius R and length L (with R << L ) possesses a uniform
0 0
volume charge density rho. Determine the electric field for
all points inside the cylinder (r < R ).
0
3. A thin charged rod of length L lies along the positive
x axis with one end at the origin. Its charge per unit length is
lambda = A x , where A is a constant. Find the electric field at a
point on the x axis, with x = b + L . [Integration hint: you
may find it useful to make a change of variables to make the
denominator in the integrand as simple as possible.]
4. A small sphere of mass m and charge q hangs as a
pendulum of length L in a region where the electric field is
directed downward and has magnitude E . Show that the period of
the pendulum is omega = sqrt(L/[ g + qE/m ]) . [Note that the expression
for omega under gravity alone is contained in this expression.]