Physics 321 -- Spring 2005
Homework #8, due at beginning
of class Wednesday March 30.
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+(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.
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 3rd Law, the force on
the sphere is equal and opposite to the force on the sheet.)