Problem 1 (10 pts)(a, 5 pts) Write the equation expressing the relation between electric force and electric field. Theequation, including correct subscripts and vector symbols, must be exactly correct–no partial credit.(b, 5 pts) Write the equation for the electric field of a point charge. The equation, including correctsubscripts and vector symbols, must be exactly correct–no partial credit.4Problem 2 (19 pts)A ping pong ball with charge of −6 × 10−8C is at the origin. The positions of locations A and B aregiven on the diagram.(a, 3 pts) Draw an arrow on the diagram above to represent the electric field at location A due to theping pong ball.(b, 3 pts) Draw an arrow on the diagram above to represent the electric field at location B due to theping pong ball. Label itEB. To receive full credit, the length of this arrow relative to thearrow you drew for part (a) must be correct.(c, 6 pts) What is the magnitude of the electric field due to the ping pong ball at location B ?(d, 4 pts) A proton is placed at location B. What is the magnitude of the force on the proton?(e, 3 pts) Draw an arrow on the diagram to represent the direction of the force on the proton. Label itF .To receive full credit, the direction of this arrow must be consistent with the electric fielddirections you previously drew.5Problem 3 (15 pts)(15 pts) A point charge of +13 μC(13× 10−6C) is located at -2, 3, -5 m. What is the electric fieldcontributed by this charge at location -6, -4, 3  m? Express your result as a three-componentvector. You must show all your work carefully in order to get credit.6Problem 4 (26 pts)Two dipoles are oriented as shown in the diagram. Each dipole consists of two charges +5 nC and -5 nC,held apart by a rod of length 1.2 mm (nC = nanocoulomb = 1 × 10−9coulomb). The location marked xis 9 cm from the center of each dipole.9 cm9 cmdipole 2dipole 1(a, 6 pts) What is the magnitude of the electric field at location A due to dipole 1 alone?(b, 3 pts) What is the direction of the electric field at location A due to dipole 1 alone? Circle one ofthe following:+x -x +y -y zero magnitude(c, 6 pts) What is the magnitude of the electric field at location A due to dipole 2 alone?(d, 3 pts) What is the direction of the electric field at location A due to dipole 2 alone? Circle one ofthe following:+x -x +y -y zero magnitude(Continued next page)7(Problem 4, continued)(e, 8 pts) A small ball carrying a charge of +8 nC uniformly distributed over its surface is placed atlocation A. What is the electric force on the ball, expressed as a three component vector? Your answermust be consistent with your answers to parts a-d to receive full credit.8Problem 5 (18 pts)In a particular region of space there is an electric fieldE1that is nearly uniform in magnitude anddirection, due to charges that are not shown in the diagram. The magnitude ofE1is 2300 N/C. Thedirection ofE1are indicated by arrows shown in the diagram below. A metal rod is placed in this region,resting on an insulating support not shown in the diagram. The mobility of the metal is 4.5 × 10−3(m/s)/(N/C). The metal has been in the electric field for a time greater than a few seconds.metal rodE1E1E1E1(a, 4 pts) What is the drift speed (or average speed) of the mobile electrons in the metal rod? Showwork, or explain briefly.(b, 4 pts) What is the magnitude of the net electric field inside the metal rod? Explain briefly how youdetermined this.(c, 3 pts) On the diagram, show the charge distribution in and/or on the metal rod, using thediagrammatic conventions discussed in the textbook and in class. If there is no distribution of charge,state this explicitly.(d, 4 pts) What is the magnitude of the electric field due only to charges in and/or on the metalrod? Explain briefly how you determined this.(e, 3 pts) On the diagram, at the location marked with the “x”, draw the direction of the electric fielddue only to charges in and/or on the metal rod?. Your answer must be consistent with youranswer to part (d) to receive full credit.9Problem 6 (12 pts)You pull a piece of magic tape off of a surface and bring it near a negatively charged plastic pen. Youobserve that the tape is repelled by the pen. You hang the tape by a thread, and bring a neutral plasticblock near the tape.(a, 3 pts) On the diagram, at location A inside the plastic, draw an arrow indicating the electric field dueto the tape. Label the arrow Etape. If it is zero, say so explicitly.(b, 3 pts) On the diagram, at location B, using the diagrammatic conventions discussed in the textbookand in class, draw the polarization of a molecule inside the plastic block. If there is no polarization, sayso explicitly.(c, 3 pts) On the diagram, at location C on the surface of the tape, draw an arrow indicating the electricfield due to the plastic block. Label the arrow Eplastic. If it is zero, say so explicitly.(d, 3 pts) On the diagram, at location D on the surface of the tape, draw an arrow indicating the forceon the tape due to the plastic block. Label the arrow F . If it is zero, say so