PHYS1212 Exam#2 Spring 2014

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1 PHYS Exam# Spring 4 NAME There are 9 different pages in this quiz. Check now to see that you have all of them. CEDIT PAT A 6% PAT B 4% TOTAL % GADE All work and answers must be given in the spaces provided on these pages. If you would like to get credit for having taken this exam, we need your name above. Please write your name clearly. If we catch you cheating on this exam, you will be given an F in the course. Sharing information about this exam with people who have not yet taken it is considered cheating on the exam for both parties involved.

2 PAT A. Each question is worth 3%. In the space provided, to the left of the question number, write the letter corresponding to the best answer to the question. C_. 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: A. the ball becomes positively charged by induction B. the ball becomes negatively charged by induction C. there is a rearrangement of the electrons in the ball D. the string is not a perfect insulator E. the number of electrons in the ball is more than the number in the rod A. Two charged particles are arranged as shown. In which region could a third particle, with charge + C, be placed so that the net electrostatic force on it is zero? A. I only B. I and II only C. III only D. I and III only E. II only E_ 3. Electric field lines: A. are trajectories of a test charge B. are vectors in the direction of the electric field C. cross each other in the region between two point charges D. form closed loops E. are none of the above _A 4. Positive charge +Q is uniformly distributed on the upper half a semicircular rod and negative charge Q is uniformly distributed on the lower half. What is the direction of the electric field at point P, the center of the semicircle? A. B. C. D. E.

3 D_ 5. A small object has charge Q. Charge q is removed from it and placed on a second small object. The two objects are placed m apart. For the force that each object exerts on the other to be a maximum. q should be: A. B. Q C. Q D. Q/ E. Q /4 D 6. To make an uncharged object have a positive charge A. remove some neutrons B. add some neutrons C. add some electrons D. remove some electrons E. heat it to cause a change of phase D 7. An electric field is most directly related to A. the momentum of a test charge B. the kinetic energy of a test charge C. the potential energy of a test charge D. the force acting on a test charge E. the charge carried by a test charge _B 8. A parallel plate capacitor of capacitance C has plates of area A with separation d between them. When it is connected to a battery of voltage V, it has charge of magnitude Q on its plates. It is then disconnected from the battery and the plates are pushed closer to a separation d/ without discharging them. After the plates are d/ apart, the magnitude of the charge on the plates and the potential difference between them are: A. Q, V D. Q, V B. Q, V E. Q, V C. Q, V C_ 9. A battery is used to charge a parallel combination of two identical capacitors. If the potential difference across the battery terminals is V and total charge Q flows through the battery during the charging process then the charge on the positive plate of each capacitor and the potential difference across each capacitor are: A. Q/ and V/, respectively B. Q and V, respectively C. Q/ and V, respectively 3

4 D. Q and V/, respectively E. Q and V, respectively C_. If both the plate area and the plate separation of a parallel-plate capacitor are doubled, the capacitance is: A. doubled B. halved C. unchanged D. tripled E. quadrupled B. An electron traveling north enters a region where the electric field is uniform and points north. The electron: A. speeds up B. slows down C. veers east D. veers west E. continues with the same speed in the same direction B_. The diagram shows the electric field lines due to two charged parallel metal plates. We conclude that: A. the upper plate is positive and the lower plate is negative B. a proton at X would experience the same force if it were placed at Y C. a proton at X experiences a greater force than if it were placed at Z D. a proton at X experiences less force than if it were placed at Z E. an electron at X could have its weight balanced by the electrical force A_3. Points and T are each a distance d from each of two particles with charges of equal magnitudes and opposite signs as shown. If k = /4πε, the work required to move a particle with a negative charge q from to T is: A. B. kqq/d C. kqq/d D. kqq /( d) E. kqq/(d) 4

5 _E 4. Which of the following graphs represents the magnitude of the electric field as a function of the distance from the center of a solid charged conducting sphere of radius? A_ 5. A Two particle with charges Q and Q are fixed at the vertices of an equilateral triangle with sides of length a. If k = /4π, the work required to move a particle with charge q from the other vertex to the center of the line joining the fixed particles is A. B. kqq/a C. kqq/a D. kqq/a E. kqq / a A 6. Two thin spherical shells, one with radius and the other with radius, surround an isolated charged point particle. The ratio of the number of field lines through the larger sphere to the number through the smaller is: A. B. C. 4 D. / E. /4 D 7. When a piece of paper is held with one face perpendicular to a uniform electric field the flux through it is 5N m /C. When the paper is turned 5 o with respect to the field the flux through it is: 5

6 A. B. N m /C C. N m /C D. 3N m /C E. 5N m /C A_ 8. Positive charge is distributed uniformly throughout a non-conducting sphere. The highest electric potential occurs: A. at the center B. at the surface C. halfway between the center and surface D. just outside the surface E. far from the sphere D 9 An electron goes from one equipotential surface to another along one of the four paths shown below. ank the paths according to the work done by the electric field, from least to greatest. A.,, 3, 4 B. 4, 3,, C., 3, 4 and tie D. 4 and tie, then 3, then E. 4, 3,, C An electron is accelerated from rest through a potential difference V. Its final speed is proportional to A. V B. V C. V D. /V E. / V 6

7 PAT B Show all your work to receive full credit. A correct answer alone is only worth point. Make sure you draw a free-body diagram if needed.. (5%) In the figure, two tiny conducting balls of identical mass m and identical charge q hang from nonconducting threads of length L. Assume that is so small that tan can be replaced by its approximate equal, sin. Show that, for equilibrium, Solution: Under equilibrium, the left figure show the Free Body Diagram (total 5pts, T and its decomposition pts, G: pt; Fe: pt; coordinate: pt), according to Newton s first law, we have F Fx i.e., Fy Thus, Tx Fe Ty G (this equation or equation below:pt) (this equation: pts; if only this equation without above equation: 3pts) q And T x T sin, T y T cos, G mg, and F e (pts) 4 x q T sin () Thus, 4 x T cos mg () Using Eq. () divided by Eq. (), one gets, q tan 4 x mg x / Since is small, tan sin, thus L x q L 4 x mg Therefore, 3 L q L q x 4 mg mg q x L mg / 3 (The derivation procedure: 4pts) y x Fe Ty T G Tx And (final answer: pt) q L x mg / 3 7

8 . (5%) Consider two thin, conducting, concentric spherical shells as shown in cross-section in the following figure. The inner shell has a radius r, and a charge of +Q; the outer shell has a radius r, and a charge of -Q. a) (%) Find the electric field E in regions A, B, and C? (pts) (pts) (pts) (pts) (pts) 8

9 b) (%) Find the electric potential V in regions A, B, and C, with V = at r = (pts) (pts) (pts) (pts) (pts) 9

10 c) (5%) Please Find the capacitance of the two shell system (pts) (3pts)

11 PAT C BONUS QUESTION (%) Two charged spherical conductors of radius = 6 cm and = cm are separated by a distance much greater than 6 cm, and are connected by a long, thin conducting wire. A total charge of Q = +8 nc is placed on one of the spheres. Assume that the charge on the conducting wire is negligible. a) (%) What is the charge on each sphere? When the two spheres are connected by a thin wire, they become equal-potential surface, i.e., the electric static potential on the two sphere shall be the same. (pts) Assuming there are Q charge in Sphere#, and Q in Sphere #, according to conservation of charge, Q Q Q () (3pts) At infinite distance from the two sphere the potential is zero, and since the potential on a q spherical conducting shell is expressed as V, (pts) we have 4 V V i.e., Q Q 4 4 or Combining Eq. () and Eq. (), we have 6 Q Q 8nC 6nC 6 Q Q nc (pts) Q Q () (3pts) b) (4%) What is the electric field near the surface of each sphere? According to Gauss law, the electric field near a surface of a charged conducting sphere is q expressed as E rˆ (pts), thus 4 9 Q E rˆ N / Crˆ. 5 N / Crˆ 4 ( 6 ) 9 Q 9 5 E rˆ N / Crˆ N / Crˆ 4 ( ) (pts) c) (4%) What is the electric potential of each sphere? Since the two spheres have the same potential, (pt) 9 Q V V V 4 6 (3pts)

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