PHYS208 Fundamentals of Physics II

Answer for Ch. 24, 4Q

a) All four charges contribute to the electric field at P, and to all other points on the gaussian surface for that matter,
b) But the total flux through the gaussian surface is directly proportional to only the net charge enclosed!

Answer for Ch. 24, 15P

Solution from HRW:
The total flux through any surface that completely surrounds the point charge is proportional to q. (I am dropping the permittivity factor for my convenience.) If you stack identical cubes side by side and directly on top of each other, you will find that 8 cubes meet at any corner. Thus one-eighth of the field lines emanating from the point charge pass through a cube with a corner at the charge and the total flux through the surface of such a cube is q/8. Now the field lines are radial, so at each of the 3 cube faces that meet at the charge, the lines are parallel to the face and the flux through the face is zero. The fluxes through each of the other 3 faces are the same to the flux through each of them is one-third the total. That is, the flux through each of these faces is (1/3)(q/8) = q/24. (Remember to reinstate the permittivity factor to get the right units!)

Last updated Mar. 1, 1998.
Copyright George Watson, Univ. of Delaware, 1998.