1. A proton approaches a Thorium nucleus (90 protons) 2.8 x 106m/s from far away. If the nucleus is xed to the origin, find the distance of closest approach (in pm) assuming the nucleus is a point particle and using conservation of energy. 2. Electric charges are fixed to points on a grid as shown. a) Find the electrical potential energy (J) of the charge configuration. b) Find the electric potential (V) at the origin from the given charges. (3) Find the work (J) it would take to bring a +6.0nC charge from far away to the origin. 3. A +56nC charge is located at the origin and is surrounded by a hollow metal sphere inner radius 2.0cm, outer radius 6.00m. The hollow sphere itself has a net charge of -24nC a) What is the charge density (C/mz) on the inner surface of the hollow sphere b) What is the charge density (C/mz) on the outer surface of the hollow sphere c) Find the electric field (V/m) at r = 40.cm (magnitude and direction) and at r = 4.00m. d) What is the electric potential (V) at r = 6.0cm? at r = 4.0cm? 4. A thin rod length L with uniform charge Q is centered at the origin lays along the xaxis (between x = -L/2 and x = + U2). 3) Derive the electric potential V for the continuous charge (show all steps) for a point x = d on the xaxis to the right of the end of the rod (i.e., d > L/2) in terms of k, Q, L, and d. b) Evaluate the electric potential (in V) at d = 30.0cm for L = 20 .Ocm and Q = 34 ac