FINAL EXAM - December 18, 1995

  1. A small metal ball of mass 1 gram is hung from a scale 1cm above a large grounded metal plate. The ball is given an electrical charge, which results in the scale reading a weight 1% larger than before the ball was charged. What is the total charge given to the ball? (The acceleration due to gravity at the Earth's surface is 9.8 m/s/s).

  2. What is the electrostatic potential inside an infinitely long square metal tube of width and height pi, with two opposing faces grounded to 0 volts, one face held at 6 volts, and the other face at -6 volts? (The edges of the "hot" plates are insulated from the rest of the tube.)

  3. What is the magnetic field everywhere (inside and out) of a coaxial cable of radius R with current I running down the center conductor and returning along the outer sheath?

  4. What is the magnetic flux through a spherical surface surrounding a permanent magnet with dipole moment m? Prove your answer from Maxwell's equations.

  5. What is the magnetic field at the center of a (hollow) ball of radius 3 cm wound with 25 loops of wire carrying a current of 0.001 amps?

  6. What is the total charge on one plate of a parallel plate capacitor filled with a dielectric characterised by K = 1.2. The plates are circular in shape, with a radius of 10 cm, are separated by 1cm, and held at a potential of 1.5 volts with respect to each other.