Physics 321 -- Spring 2006

Homework #8, due at beginning
of class Wednesday March 29.

1. [4pts] Marion & Thornton, problem 5-2 (Same in Edition 4).

2. [4pts] Marion & Thornton, problem 5-4 (Same in Edition 4
except they forgot to mention that the particle starts at rest.)

3. a) [4pts] Marion & Thornton, problem 5-7 (Same in Edition 4).

b) [4pts] 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+(2*R*/*l*)^{2})^{1/2} to first order in
(2*R*/*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.

4. [4pts] Marion & Thornton, problem 5-13 (Same in Edition 4).

5. [4pts] Marion & Thornton,
problem 5-15 (Same in Edition 4).

6. [4pts] Marion & Thornton: problem 5-16 (Same in Edition 4).
(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 3^{rd} Law, the force on
the sphere is equal and opposite to the force on the sheet.)