EXAM 1 March 18, 1998 PHYS 208

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g = 9.8 m/sec^{2} |
Radius of the earth = 6.38 x 10^{6} m |
The mass of the electron is 9.11 x 10^{-31} kg. |

1 -------------- = 9.0 x 10 |
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 R_{1} and
R_{2} 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.]