FINAL EXAM - December 13, 1996

  1. How far below an infinite conducting plate must a proton (mass = 1.67e-27 kg) be placed in order that the electrostatic attraction upward toward the plate is balanced by the gravitational force downward? (The acceleration due to gravity at the Earth's surface is 9.8 m/s/s).

  2. What is the capacitance of the Earth (Radius = 6.4e+06 m)? The Earth carries a negative charge that gives a field of about 100 V/m at the surface. What is the total charge on the Earth? Calculate the potential at the surface of the Earth.

  3. A wire of radius R carries a steady current I distributed uniformly across the circular cross section of the wire. What is the magnetic field both inside and outside the wire?

  4. Find the electric field a distance z above the center of a flat circular disc of radius R, carrying a uniform surface charge.

  5. If the disc in the previous problem is set spinning with a rotational frequency omega, what is the magnetic field a distance z above the center?

  6. A thick spherical shell (inner radius a and outer radius b) is made up of dielectric material with a frozen in polarization P = kr. Calculate and locate all the bound charges, and use them to find the electric field everywhere. Calculate the electric displacement everywhere, and use it to find the electric field.