The gure shows a fixed {non-moving] charge Q 2::- and four I .. " ' ' "' a; points, A1 B, C, and D. Points A and D are the same distance Ii \"x from charge Q and points B and C are the same distance from \\ __ I charge Q. Point B is directly between point A and Q and point C C'- 'K '1 is directly between point D and Q. 0 'sie The dashed lines are on circles centered at the charge Q. Mechanics Reminder: Potential Energy: Consider two objects in a system interacting by a conservative force TEE]. 1where i: is a displacement 1rector pointing from one object to another. {In this problem, 1: is a 1sector pointing from Q to other positions.) [fthe objects moye such that 1" changes by a small amount all: there is a small change in the potential energy of the system related to the force F: dPEE = Elia-d! = |F{r)| ldi] cos cos BF. '3 This is the dot {scalar} product ofthe 1rectors Eand dsee Section 1.19). H is the as: angle between the force 1'? and the displacement d: This recitation is a study of \"Eleclric Potential Energy", the energy related to the electric force on charges. D) Using the expression for the change in potential energy above and using the Coulomb Force between point charges, set up and solve an integral for the change in Electric Potential Energy of the system (proton and Q) as the proton moves from point C to point D. Write your answer in terms of the positions of points C and D, R and R . Hint: In this case the proton is moving in the radial direction, dl = dr and Q > 0, q proton oton = e > 0. What is the change in the Electric Potential Energy of the system as the proton moves from Point A to Point B? No calculation is needed but explain your answer. E) A proton starts at rest at point C and is released. In this case there are no other (important) forces on the proton once the proton is released (gravity can be neglected). You want to calculate the speed of the proton when it reaches point D. What will happen to the proton? Explain and setup the physics to give as much information as you can without doing any calculations. Consider the forces and changes in the energy of the system. Again, assume the charge Q does not move. Hint: You must use conservation of mechanical energy to solve this problem. G) If the point C is 10 cm from charge Q, point D is 20 cm for the charge, and Q = + 2 pC, what is the speed of the proton at point D