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 −9 × 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 itEB. 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 itF .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 +17 μC(17× 10−6C) is located at -4, 6, -10 m. What is the electric fieldcontributed by this charge at location 5, -2, -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 +7 nC and -7 nC,held apart by a rod of length 1.3 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 fieldE1that is nearly uniform in magnitude anddirection, due to charges that are not shown in the diagram. The magnitude ofE1is 1700 N/C. Thedirection ofE1are 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
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