True or False questions. Determine whether or not each of thefollowing statements is true. If a statement is true, prove it. Ifthe statement is false, provide a counterexample and explain how itconstitutes a counterexample. Diagrams can be useful in explainingsuch things.
1. A sphere of radius R is centered at the origin. A totalcharge Q is uniformly distributed throughout its interior. A ballof radius R/2 centered at the the origin is carved out anddiscarded, leaving behind an empty cavity. The electric potentialhas the same value at every point inside the cavity.
2. A sphere of radius R is centered at the origin. A totalcharge Q uniformly distributed throughout its interior. A ball ofradius R/2 centered at the point (x,y,z) = (0, 0,R/4) is carved outand discarded, leaving behind an empty cavity. The electricpotential has the same value at every point inside the cavity.
