Physics 321 -- Spring 2004
Homework #8, due at beginning
of class Wednesday March 31.
1. [4pts] Marion & Thornton: problem 5-1. To answer the last question in this problem,
think about electrostatics.
2. [4pts] Marion & Thornton, problem 5-2. (One way to do this problem -- but not the
easiest way -- is to use the differential form of Gauss’s
Law, which is Eq. 5.37 in the textbook.
To calculate the divergence of a vector field in spherical coordinates,
see Eq. F.18 in Appendix F.)
3. [3pts] Marion & Thornton, problem 5-4.
(Assume the particle starts at rest.)
4. a) [3pts] Marion & Thornton, problem 5-7.
b) [3pts] From your result in part (a), use the Taylor
series expansion to evaluate the potential very close to the rod, i.e. in the
limit R << l. You should expand the
quantity (1+(2R/l)2)1/2 to first order in
(2R/l)2. Then take
the gradient of the potential to find the gravitational field. The result should look familiar from
electrostatics -- the electric field of an infinitely long charged rod.
5. [3pts] Marion & Thornton, problem 5-13.
6. [4pts] Marion & Thornton,
problem 5-15.
7. [4pts] Marion & Thornton: problem 5-16.
(You can use the method of Example 5.3 in the book.
You can check your answer by using Gauss’s Law to calculate the
gravitational field g due to the infinite sheet of charge.
From that you can find the force on the sphere.
By Newton’s 3rd Law, the force on
the sphere is equal and opposite to the force on the sheet.)