(b: 5 pts) A thin plastic rod of length 4.5 m has been rubbed with a wool cloth, and has gained a net charge

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1 Problem 1 (25 pts). (a: 5 pts) student claimed that the formula for the electric field outside a cube of edge length L, carrying a uniformly distributed charge Q, at a distance x from the center of the cube, was Q E = L. Explain how you know that this formula cannot be correct. ε 0 x (b: 5 pts) thin plastic rod of length 4.5 m has been rubbed with a wool cloth, and has gained a net charge 7 of 3 10 coulombs, distributed uniformly over its surface. cubical block of copper with side length 0.07 m is placed with its center 0.12 m from the center of rod, as shown in the diagram below. Note that the rod is very long, and only part of it is shown on the diagram. On the diagram, show the distribution of charges in and on the copper, using the conventions discussed in the textbook m 0.07 m (c: 5 pts) On the diagram above draw an arrow representing the electric field at the center of the copper block, due only to the charges in and on the copper. (d: 10 pts) What is the magnitude of the electric field vector you drew in part (c)? Show your work, and explain.

2 Problem 1 ( 12 pts) (a: 4 pts) The magnitude of the electric field due to a small dipole is measured to be 250 N/C at a location on the axis of the dipole, 2 cm from the center of the dipole. pproximately what is the magnitude of the electric field due to the dipole at a location 6 cm from the dipole, along the same axis? Show your work. (b: 4 pts) The magnitude of the electric field due to a uniformly positively charged disk of radius 4 m is measured to be 3000 N/C at a location in the air 6 mm from the center of the disk, along a line perpendicular to the disk. pproximately what is the magnitude of the electric field due to the disk at a location 9 mm from the center of the disk, on the same line? Show your work. (c: 4 pts) The magnitude of the electric field due to a uniformly negatively charged thin plastic rod of length 2 m is measured to be 970 N/C at a location near the middle of the rod, at a location 8 cm from the rod, on a line perpendicular to the rod. pproximately what is the magnitude of the electric field at a location 4 cm from the rod, on the same line? Show your work. Problem 2 ( 12 pts) t each of the the locations marked by a letter (, B, C) in the diagram below, draw an arrow representing the net electric field at that location. longer arrow should represent a field with larger magnitude. B C 2

3 Problem 4 (35 pts). 6 glass disk carries a positive charge of distributed uniformly over its surface. Its center is at the origin, and its radius is R = 7 m. small hollow plastic ball, of radius 0.02 m, carrying a charge of C 8 uniformly distributed over its surface, is located with its center at 0.07, 0.04, m. (a: 23 pts) Calculate the net electric field at location y 0.05, 0.1,. Show every step in your calculation explicitly. Give your answer as a vector. R (not to scale x (b: 5 pts) Draw the electric field vector you calculated on the diagram, with its tail at the observation location. (c: 2 pts) Explicitly state any approximations or assumptions you made in your calculation. (c: 5 pts) What would be the force on an antiproton (whose charge is e and whose mass is the same as the mass of a proton) if it were located at 0.05, 0.1,?

4 Problem 4 (18 pts) small, very lightweight hollow aluminum ball is suspended from a cotton thread. The events depicted in frames 1-6 then occur, in sequence. ll diagrams show cross-sectional views of the objects. For each frame (1-6), write the letter of the corresponding diagram (-P) that best depicts the distribution of charge in and/or on the aluminum ball, following the conventions for diagrams discussed in the textbook and in class. Some letters may be used more than once; others may not be used at all. 1. You touch the ball briefly with your fingers, then release it. 2. Holding only the thread, you bring the ball near a charged metal block. 3. The ball swings toward the block. Ball diagram: Ball diagram: Ball diagram: Negatively charged plastic pen 4. The ball briefly touches the block. 5. The ball swings away from the block. 6. The ball is repelled by a negtively charged plastic pen. Ball diagram: Ball diagram: Ball diagram: Diagrams showing distribution of charge in and/or on the aluminum ball. Only patterns are shown, not magnitudes: both distributions at right would be represented by diagram. or B C D E F G H I J K L M O P 4

5 Problem 3 (15 pts) The arrangement of charged particles shown in the diagram is called an electric quadrupole. t locations on the x axis far from the quadrupole, the electric field due to the quadrupole has the form: 1 E = h ---- ( h is a constant with units, combining the magnitudes of the charges, and their separations). 4πε 0 x 4, 0, C m 2 The diagram below is not drawn to scale; both locations and B are far from the quadrupole. The origin is at the center of the quadrupole. + + < 0, 0, 0> < a, 0, 0> B <b, 0, 0> (a: 2 pts) t two locations between and B, draw arrows showing the electric field at that location. The relative magnitudes of the arrows should be correct (longer arrow means larger magnitude). (b: 3 pts) Is V B V positive, negative, or zero? Briefly but clearly explain your reasoning: (c: 10 pts) What is V B V? Your answer should be a symbolic (algebraic) expression, which may include the constants h, a, b, and 1 ( 4πε 0 ). Show all steps in your work. 4

6 Problem 8 (Bonus: 5 pts) This bonus problem is worth only 5 points, so don t work on it until you have completed and checked your work on all of the other problems in the test. long rod of length L carries a uniform negative charge Q. In the diagram,, B, and C are locations. a, b, and c are distances. Calculate the potential difference V V C. Your answer should be a symbolic (algebraic) expression. ll of the distances are small compared to L. Explain your work carefully. Uniform charge Q c b L C B a 6