Answer Happy

1. A gaussian surface in the shape of a cube is drawn around a charge of +12nC, at the center of the cube. Calculate the flux of the electric field from this charge through one of the cube's faces.

2. Calculate the electric potential energy from this familar charge configuration, in terms of €0, e and a. Please simplify your answer to receive full credit.

3. Suppose that the electron were not a perfect point particle, but a charge distribution extended over space. Then, the interactions of the bits of negative charge making up the electron would give rise to a total electric potential energy E of the electron. In turn, there would be a contribution to the electron mass through the famous equation E = mc2. So, a not-too-ridiculous theory of the origin of the electron's mass is that it comes entirely from its electric potential energy. The question is, what is the size of the electron in this theory? Is it reasonable? To answer this question, first derive something more general: write a formula for the total potential energy of a sphere of radius a and total charge Q uniformly distributed throughout its volume. Express the result in terms of €0, Q and a. This involves some Calculus. If you get lost in the weeds, this is the "classical electron radius” problem, which you can look up. Answer: Using what you found in the last question, assuming that the electron is a sphere of uniform charge density, calculate what its radius would have to be to be in order for its stored electrical potential energy to be responsible for its mass through E = mc2 (do calculate a number here - it's quite an interesting result and indicates whether the theory makes sense)