EXAM 1 March 12, 1997 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 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 *a _{0}*. 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 - xbetween