Overview
You have a very (infinitely) long solid conducting cylinder with length L, base radius R, and total charge +Q.
(a) Use Gauss’s law to find the electric field vector inside and outside the cylinder. Explain your reasoning. You can give a verbal description of the electric field vector direction.
(b) Similar to how we found the electric field outside a conducting sphere to look like that of a point particle, what does the electric field outside the cylinder look like?
(c) Would the electric field inside the cylinder stay the same if the cylinder was instead insulating and uniformly charged? Explain why or why not?
Question 2
2 electrons and 2 positrons are fixed at the corners of a square with sidle length a, as shown in the attached figure. (Treat all particles as point particles, and ignore gravity).
(a) Find the total electric field vector due to the 4 charges at the origin (which is that center of the square). Hint: you can leverage symmetry, or find each electric field vectors individually then add them up.
(b) Find the total electric potential due to the 4 charges at the origin.
(c) Find the total electric potential energy of the setup. (d) if an alpha-particle is placed at the origin, what is the electric force it would experience due to all 4 charges?