Page 1 of 6 Physics II Exam 1 155 points Name Discussion day/time Pat I. Questions 110. 8 points each. Multiple choice: Fo full cedit, cicle only the coect answe. Fo half cedit, cicle the coect answe and one incoect answe. Fo ¼ cedit, cicle the coect answe and two incoect answes. 1. Two small sphees epel one anothe electostatically. Which of the following must be tue? a. Both have the same chage. b. Neithe is chaged. c. Both ae chaged. d. At least one sphee is chaged. e. They ae oppositely chaged. 2. Thee chages q, Q, and Q ae placed at the cones of an equilateal tiangle as shown. The net foce on chage q due to the othe two chages is a. vetically up q b. vetically down. c. zeo. d. hoizontal to the left. e. hoizontal to the ight. Q Q 3. A positive chage is bought close to a fixed neutal conducto that has a cavity. The cavity is neutal; that is, thee is no net chage in the cavity. Which of the figues best epesents the chage distibution on the inne and oute walls of the conducto? 5 e. 5 1 2 3 4 4. A long box of length l, width w, and height h contains a line of positive chage density λ. The line of chage is oiented paallel to the length of the box, is centeed within the box, and is length l/2. The net electic flux though the box is a. zeo b. positive c. negative d. not enough infomation given e. positive though one end, and negative though the othe

Page 2 of 6 5. Fou chages of equal magnitude ae aanged at the cones of a squae. In which aangement is the magnitude of the electic field at point P a maximum? P P P P 1 2 3 4 e. The maximum electic field occus in moe than one of these aangements. 6. Which point in the electic field is at the highest potential? 1 5 2 3 e. 5 4 E 7.A spheical shell of adius b contains at its cente a metal sphee with adius a. The sphee has chage q wheeas the shell has chage q. Which gaph best epesents the potential as a function of adius? Assume the potential is zeo at infinity. e. 5 f. 6 1 2 3 4 q q a b 5 6

Page 3 of 6 8. The chage on each capacito in a set of capacitos in paallel is a. diectly popotional to its capacitance. b. invesely popotional to its capacitance. c. independent of its capacitance. d. the same. e. None of these is coect. 9. The capacitance of a capacito a. is defined as the amount of wok equied to move a chage fom one plate to the othe. b. deceases if a dieletic is placed between its plates. c. is independent of the distance between the plates. d. has units of enegy/chage. e. is independent of the chage on the capacito. 10a. (4 points) If a dieletic is inseted between the plates of a paallelplate capacito that is connected to attey, the a. voltage acoss the capacito deceases. b. electic field between the plates deceases. c. electic field between the plates inceases. d. chage on the capacito plates deceases. e. chage on the capacito plates inceases. 10b. (4 points) If a dieletic is inseted between the plates of a paallelplate capacito that is not connected to attey, the a. voltage acoss the capacito deceases. b. electic field between the plates deceases. c. electic field between the plates inceases. d. chage on the capacito plates deceases. e. chage on the capacito plates inceases.

Page 4 of 6 Pat II. Shot answe/sketch. Answe questions 1113 as completely as possible. Show you wok to ean patial cedit! 11. (25 points) A positive chage q 1 lies at the oigin, an unknown chage q 2 lies at (d 1,0), and anothe unknown chage q 3 lies at (d 2 cosθ,d 2 sinθ). All thee chages ae fixed in place. The net electic foce on q 1 is in the negative ydiection. y d 1 a. What is the sign of the chage q 2? q 1 d 2 θ q 2 x q 3 b. What is the sign of the chage q 3? c. What is the foce on q 1 due to q 2? Expess you answe in tems of k, θ, q 1, q 2, d 1, and d 2 (all paametes may not apply). d. What is the foce on q 1 due to q 3? Expess you answe in tems of k, θ, q 1, q 3, d 1, and d 2 (all paametes may not apply). e. Suppose that the magnitude of q 3 is 2q 1. What is q 2? Expess you answe in tems of k, θ, q 1, d 1, and d 2 (all paametes may not apply).

12. (25 points) A slab of unifom thickness d, fom d/2 to d/2 along the xaxis, extends infinitely in the y and z diections, as shown. The slab has unifom volume chage density ρ. The electic field is zeo in the middle of the slab, at x=0. a. Which of the following statements is tue of the electic field at the suface of one side of the slab? 1. The diection of E is constant, but its magnitude vaies acoss the suface. 2. Both the magnitude and diection of E ae constant acoss the entie suface. 3. The diection of E vaies acoss the suface, but its magnitude is constant. 4. Both the magnitude and diection of E vay acoss the suface. b. The suface nomal points in the x diection on one side of the slab, and in the x diection on the othe. What is the angle θ that the field E makes with espect to the suface nomal? (the answe is the same fo eithe side). c. To calculate E on one of these sufaces, we'll use Gauss' Law. Descibe the location and shape of you choice fo the Gaussian suface. ρ d x=0 d. What is the total enclosed chage within you suface? y x z e. What is E at the suface? f. Sketch the magnitude of the electic field as function of x. E x=d x=0 x=d x Page 5 of 6

Page 6 of 6 13. (25 points) A hollow cylinde o adius and height h has a total chage q unifomly distibuted ove its suface. The axis of the cylinde coincides with the zaxis, and the cylinde is centeed at the oigin. We will calculate the electic potential at the oigin by summing up the individual potentials due to infinitesimally thin ings. a. Conside a thin ing of thickness dz at a distance z above the oigin, as shown. What is the distance fom the oigin to the ing? b. How much chage is contained in the ing? z dz c. What is the potential d at the oigin due to this ing? d = z=0 h d. To obtain the total potential, you need to integate ove d. What ae the lowe and uppe limits of this integal? e. Evaluate. You may find the following useful: da/(a 2 b 2 ) ½ = ln{a/b(1a 2 /b 2 ) ½ } da/(a 2 b 2 ) = 1/b tan 1 (a/b) da/a = ln(a) z = y x f. What is the potential in the limit that h? This can be solved mathematically o conceptually.