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EXAM 1                         March 12, 1997                         PHYS 208
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Name:________________________________________________________

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Code:_____________________

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.

 g = 9.8 m/sec2 Radius of the earth = 6.38 x 106 m The mass of the electron is 9.11 x 10-31 kg. ``` 1 -------------- = 9.0 x 109 N m2/C2 4 pi epsilon0 ``` e = 1.60 x 10-19 C
For all problems, place the equations representing the physics principles you are using in the box on the page. You may use the general form of the equation or the form you get applying the principle to the problem at hand. If no diagram is applicable to a problem, write "none" in the diagram section.

1. (10 points)
(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 the relationships among Force, Electric Field, Potential Energy, and Electric Potential.

2. (30 points) In the Bohr model of the hydrogen atom, an electron circles a proton at a radius of a0. How fast must the electron be moving if no forces other than the Coulomb attraction are large enough to matter?

3. (From homework, 30 points) An infinitely long nonconducting cylindrical shell of inner radius a and outer radius b has a uniform volume charge density rho . Find the electric field for all  r < b .

4. (30 points) What is the total potential energy due to electric forces of two uniformly charged rods of length L placed along the x-axis a distance a apart? Express your answer in terms of the integral of

```                       2 L + a - x
ln ------------ dx
L + a - x
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between x = 0 and x = L.