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EXAM 1                         March 18, 1998                         PHYS 208
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Name:________________________________________________________

If you would like your grades included in an EMail message to the entire class to be sent out as soon as the grading is done, enter a 6-8 character code suitable for public use below. The grades will be listed in the message by code only -- no names. Remember the code, for I will use it all semester unless you ask me to stop.

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

1. (10 points)
(a). Describe a good way to reconstruct Gauss's Law, including the placement of the constant in the law. You may assume that you know Coulomb's Law.

(b). Explain the relationships among Force, Electric Field, Potential Energy, and Electric Potential.

2. (30 points) [Slightly simplified from homework] Three equal charges Q are at the corners of an equilateral triangle of side L. The charges are released one at a time proceeding clockwise around the triangle. Each charge is allowed to reach its final speed a long distance from the triangle before the next charge is released. What is the final kinetic energy of (a) the first charge released, (b) the second charge released, and (c) the third charge released?

3. (30 points)
(a) What is the electric field between the plates of a cylindrical capacitor of length L carrying a charge Q on each plate? The radii of the inside and outside cylinders are R1 and R2 respectively, and there is a dielectric of dielectric constant kappa between the plates.

(b) What is the magnitude of the potential difference between the plates of this capacitor?

(c) What is the capacitance of this device?

4. (30 points) Six equal point charges q are placed at the corners of a regular hexagon of side a.
(a) What is the value of the electric field at the center of the hexagon?

(b) One of the charges is removed from its corner. Show that the new electric field at the center points toward the vacant corner and find its magnitude.

[This problem requires thought, not calculation. If you find yourself tempted to do a lot of algebra, write down your starting equation(s) and tell what algebra you need to work out, but do not undertake the algebra. I will give partial credit accordingly. Full credit is reserved for completing the problem with minimal algebra.]