EXAM 1 March 12, 1997 PHYS 208
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|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 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 - xbetween x = 0 and x = L.