Show all your work. Partial credit can only be given if you show your work and can follow it. Correct answers with no work shown receive no partial credit. The point value for each problem is given. Use three significant figures for all your answers. You must include correct units in all your answers. 1. A ball with a charge of -2.00 nC is located at x = -3.00 m. Treat the ball as a point charge. (a) What is the electric field the ball produces at x = 2.00 m? Give answer in vector form. (5 points) (b) A second ball with a charge of -2.50 nC is placed at x = 2.00 m. What is the force the electric field exerts on this ball? Give answer in vector form. (5 points) Two charges are arranged as shown in the figure. What value of O will result in a zero electric field at P. The knowns are ke, a, q, and d. (10 points) Q= ? -39This is #92 from PS 4 3. An electron and a proton, each starting from rest, are accelerated by the same uniform electric field of 200 N/C. Determine the distance and time for each particle to acquire a kinetic energy of 3.2 x 10-16 J. (15 points) 4. Two point charges and a thin ring with radius R are arranged as shown in the figure. The axis of the ring is along the z axis. Find the magnitude of the electric field at the origin. The knowns are ke, R, and q. (15 points) R R5. Two point charges are arranged along the y axis as shown in the figure. Find the magnitude of the electric field at (12.0, 0) cm. (15 points) - -2.00 nC 5.00 cm 5.00 cm + 1.50 nC6. A thin rod with length L is placed along the y-axis as y shown in the figure. The midpoint of the rod is at the origin. The rod has been given a non-uniform charge density given by a - 4() + d' ); dq 20, where do is a dE P positive constant. Find the magnitude of the electric X field at P, which is at (d, 0) . Start with dE = k dq d . 2 and dE integrate. The knowns are ke, 10, d, and L. Use dq symmetry to simplify the problem. Hint: The integration will be very simple, if set up correctly. (15 points)