2. Recall from class that I mentioned numerous times that one can view a charged sphere (hollow or solid) as a point charge at the center of that sphere, and hence we can apply the formula kQ p2 E V= for both point charges and spherical charged bodies (but NOT for an arbitrary shape). This is a consequence of the Newton's Shell Theorem derived from the principle of su- perposition, inverse-square law and spherical symmetry. Specifically, the theorem states that¹ or Challenge: kQ T (i) A spherically symmetric body affects external objects electrically as though all of its charge were concentrated at a point at its center. (ii) If the body is a spherically symmetric shell (i.e., a hollow ball), no net electric force is exerted by the shell on any object inside, regardless of the object's location within the shell. Prove the above statements using Gauss' law. Prove the above statements using integration.

2. Recall from class that I mentioned numerous times that one can view a charged sphere (hollow or solid) as a point charge at the center of that sphere, and hence we can apply the formula kQ p2 E V= for both point charges and spherical charged bodies (but NOT for an arbitrary shape). This is a consequence of the Newton's Shell Theorem derived from the principle of su- perposition, inverse-square law and spherical symmetry. Specifically, the theorem states that¹ or Challenge: kQ T (i) A spherically symmetric body affects external objects electrically as though all of its charge were concentrated at a point at its center. (ii) If the body is a spherically symmetric shell (i.e., a hollow ball), no net electric force is exerted by the shell on any object inside, regardless of the object's location within the shell. Prove the above statements using Gauss' law. Prove the above statements using integration.