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1 Name: Sectè èor TA nameè: Student Id è Please æll in your name, student id number, section number and FORM on your test scan forms. PHYSICS 22 FALL 1997 FIRST MIDTERM EXAM, FORM A 1. You are given two point charges 1 and 2 of magnitude 6çC and,8çc respectively. 1 is placed on the y-axis 3:m away from the origin. 2 is placed on the x-axis 2:m away from the origin. aè What is the magnitude of the resulting electric æeld at the origin? bè What is the angle that the æeld makes with the positive direction of the x axis? Aè 19; N=C, 18 æ Bè 19; N=C,,18 æ ècorrectè Cè 24; N=C, 24 æ Dè 12; N=C, 18 æ Eè 12; N=C, 45 æ 3m 6 µ C 2m -8 µ C 2. A neutral metal ball is suspended by a string. A positively charged insulating rod is placed near the ball, which is observed to be attracted to the rod. This is because: Aè the ball becomes positively charged by induction Bè the ball becomes negatively charged by induction Cè the number of electrons in the ball is more than the number in the rod Dè the string is not a perfect insulator Eè there is a rearrangement of electrons in the ball ècorrectè 1

2 3. The ægure shows two suare arrays of charged particles. The suares, which are centered on point P, are misaligned. The particles are either separated by d=2 or d=4 along the perimeters of the suares. What is the magnitude and direction with respect to the postitive x-axis of the net electric æeld at the point P? Aè 3 2çæ d 2 ; 9æ -2 Bè 1 çæ d 2 ; 6 22æ Cè 1 çæ d 2 ; 18æ ècorrectè Dè 3 2çæ d 2 ; -3 18æ Eè 1 2çæ d 2 ; 18æ -2 - P 2 - y 3 - x d The ægure shows two charges 1 = 2 = 2çC held at a æxed distance d = 2m apart. A third charge 3 = 4çC is brought and placed as shown in the ægure, forming an euilateral triangle with the other two. What is the magnitude and direction èwith respect to the positive x axisè of the total electrostatic force on 1? y Aè 2:4N; 131 æ ècorrectè Bè 2:7N; 152 æ x Cè :9N; 9 æ 1 d Dè :9N; 47 æ Eè 2:7N; 18 æ d 3 2 d 2

3 5. Consider two positive charges. One is placed at the origin and the other a distance d along the vertical y axis upwards. Consider a point along the y axis such that y ç d. An approximate expression for the electric æeld at that point is, Aè 1 2çæ Bè 1 2çæ Cè 1 Dè 8çæ 1 2çæ y 2 y 3 y 2 Eè 1 4çæ y y 1=2 ècorrectè 6. A thin 4m long rod has a charge per unit length ç and lies along the y axis from y = to y = 4m. What is the magnitude of the x component of the electric æeld at x =2m; y =. Aè R 4 Bè R 4 Cè R 4 Dè R 4 Eè R 4 2çdy 4çæ è4 y 2 è ècorrectè 3=2 çdy 2çæ è4 y 2 è 2=3 çdy 4çæ è4 y 2 è 2 çdy 4çæ è4 y 2 è 1=2 dy 4çæ çè4 y 2 è 2=3 7. Positive charge is uniformly distributed along a semicircular rod. What is the direction of the electric æeld at the center of the semicircle P? Aè " Bè è Cè è Dè! ècorrectè Eè è P 3

4 8. The diagram shows four possible orientations of an electric dipole in a uniform electric æeld E. ~ Rank them according to the magnitude of the torue exerted on the dipole by the æeld, least to greatest. Aè 1; 2; 3; 4 Bè 4; 3; 2; 1 Cè 1; 2; 4; 3 Dè 3; 2 and 4 tie; then 1 Eè 1; 2 and 4 tie; then 3 ècorrectè p p p E E E 4 p E 9. The ægure shows, in cross section, three cylinders. Each cylinder carries a total charge. Concentric with each cylinder is a cylindrical Gaussian surface, all three with the same radius. Rank the gaussian surfaces according to the electric æeld at any point onthesurface, greatest ærst. Aè 1; 2; 3 Bè 3; 2; 1 Cè 1; 2 and 3 tie Dè 1 and 2 tie; Eè 1 and 2 and 3 all tie ècorrectè cylinder Gaussian Surface 4

5 1. Which of the following graphs represents the electric æeld as a function of the distance from the center of a solid conducting sphere of radius R carrying an excess positive charge? èe is correctè R R R R R A B C D E 11. Charge is distributed uniformly throughout an insulating sphere of radius R. The magnitude of the electric æeld at a point R=2 from the center is, Aè 4çæ R 2 Bè çæ R 2 3 Cè 4çæ R 2 Dè ècorrectè 8çæ R 2 Eè none of these 12. A ball of charge 5e lies at the center of a hollow metal shell that has a net charge of 1e. What is the charge on èaè the shell's inner surface and èbè its outer surface? Aè,5e, 5e Bè e, 1e Cè 1e, Dè,5e, 15e ècorrectè Eè 15e,,5e 5

6 13. A total amount of positive charge is placed on a conducting shell with inner radius R 1 and outer radius R 2. A point charge is placed at the center of the cavity. The magnitude of the electric æeld at a point outside the shell a distance r from the center is, r Aè 4çæ R 3 1 Bè 4çæ èr 2 1, r 2 è Cè 4çæ r 2 è è Dè ècorrectè 4çæ r 2 è è Eè 4çæ èr 2 1, r 2 è 14. Two inænite parallel plates carry a charge density ofç Coulèm 2 each and are placed nearby each other. Rank the points 1 through 5 according to the magnitude of the electric æeld, from smallest to largest Aè 1; 2; 3; 4; 5 Bè 5; 4; 3; 2; 1 Cè 1; 4 and 5 tie; then 2 and 3 tie Dè 2 and 3 tie; then 1 and 4 tie; 5 Eè 2 and 3 tie; then 1 and 4 and 5 tie ècorrectè 6

7 15. The ægure shows a suare array of charged particles, with distance d between adjacent particles. What is the electric potential at point P at the center of the suare if the electric potential is zero at inænity? 18 Aè 4çæ d Bè,4 Cè 4çæ d ècorrectè 7 4çæ d Dè Eè none of the above P d Two charges are æxed at the vertices of an euilateral triangle with sides of length a. The work èdone by an external agentè reuired to move from the other vertex to the center of the line joining the æxed charges is, Aè,2 4çæ a Bè 4 4çæ a Cè 4çæ a 2 Dè 2 4çæ a ècorrectè Eè,4 4çæ a a a a 7

8 17. A circular plastic rod of radius R has a positive charge uniformly distributed along one uarter of its circumference and a negative charge,6 uniformly distributed along the rest of the circumference. With V = at inænity, what is the electric potential at the center C of the circle? Aè,17p 2 4çæ 2çR Bè,5 4çæ R ècorrectè Cè,17 4çæ R 2 Dè,5p 2 4çæ R Eè -6 C R 18. In a certain situation, the electric potential varies along the x axis as shown in the graph. Rank the various intervals ab, bc, cd, de and ef according to the value of the x component ofthe electric æeld along the interval, from larger to smaller. Aè ab; bc; cd and de tie; ef Bè ab and cd and de tie; bc; ef Cè ef; de and cd tie; bc; ab ècorrectè Dè ef; ab; bc; cd; de Eè none of the above a b c V d e x f 8

9 19. A conducting ball of radius a with charge is placed in the center of a hollow conducting shell with interior radius b and exterior radius c with no net charge. Which of the following diagrams represents the electric æeld as a function of r? c a b A B a b c a b c C D E a b c a b c a b c èc is correctè 2. Initially, two point charges A =4çC; B =4çC are situated at the opposite corners of a suare of 1m each side, as shown in the ægure. Two additional charges C =2çC and D =2çC are brought from inænity to the other two corners of the suare. What is the change in potential energy of the system? Aè 28.8 J Bè 52.7 J Cè 31.4 J ècorrectè Dè 41.7 J Eè 45.8 J 9

10 = 4 µ C Α = 2 µ C C 1 m = 2 µ C D = 4 µ C Β 1