Name: Student number: Academic Honesty: In accordance with the Academic Honesty Policy (T10.02), academic dishonesty in any form will not be tolerated. Prohibited acts include, but are not limited to, the following: making use of any books, papers, electronic devices or memoranda, other than those authorized by the examiners. speaking or communicating with other students who are writing examinations. copying from the work of other candidates or purposely exposing written papers to the view of other candidates. Question # Mark Maximum Mark Multiple Choice 20 11 10 12 10 Total = /40 Enter your answers to the multiple choice questions here by blackening in the circle corresponding to the best answer. There is only one correct answer per question. [Two points each] 1. A B C D E 2. A B C D E 3. A B C D E 4. A B C D E 5. A B C D E 6. A B C D E 7. A B C D E 8. A B C D E 9. A B C D E 10. A B C D E 1
There are 10 multiple choice questions. Select the correct answer for each one and mark it on the bubble form on the cover sheet. Each question has only one correct answer. (2 marks each) 1. For questions 1 and 2: Five small identical metal balls are hung from insulating silk threads and are handled only by the threads. They are not allowed to touch one another during the following experiment. It has previously been found that none of the balls is affected by a magnet. The balls are brought near each other, and the following observations are recorded: (a) kq 1 x 1 /(x 2 1 + y2 a) 3/2 correct (b) kq 1 x 1 /(x 1 + y a ) 3 (c) kq 1 /x 2 1 (d) kq 1 x 1 /(x 2 1 + y2 a) (e) None of the above. (x 1,0) (0, y a ) Metal balls II and V exert no force on each other. Metal balls I and III repel each other. All other pairs of metal balls attract one another. For example, ball I attracts balls II, IV, and V, I II III IV V In which pairs of balls do both balls carry charge of the same sign? (a) I and II (b) I and III correct (c) I and IV (d) II and IV (e) II and V 4. A conservative force field is one in which the work needed to move an object from one point to another in the field does not depend on the path taken between the two points. In which case(s) is it true that the electric field is conservative? (a) The field of an infinite uniform plane of charge. (b) The field of an infinite uniform distribution of charge on a straight line (c) The field of any spherically symmetric distribution of charge (d) None of the above (e) All of the above correct 5. You wish to measure the electric work done on a heater by a battery, for which purpose you select an ammeter (A) and a voltmeter (V). Which of the circuits shown below would you use? 2. In which of the following pairs of balls do the two balls carry charge of the opposite sign? (a) III and V (b) I and V (c) II and III (d) I and IV correct (e) IV and V 3. A positive charge q 1 is on the x axis at (x 1, 0). Which formula represents the x component of the electric field at a point on the y axis at position (0, y a )? (k is Coulomb s constant.) 6. In the circuit below you don t know the strength of the battery or the value of any of the four resistances. Select the expression that will be equal to the voltage of the battery in the circuit. If 2 or more are true, or none are true, choose (e). 2
(a) V A + V B (b) V A (c) V A + V B + V C + V D B 9. The figure shows the equipotential lines of the electric potential that result from a charge distribution in the plane of the paper. At which location will an electron (q = 1.6 10 19 C) experience a force directed toward the top of the screen? (d) V A +V B +V D correct (e) No single one of the above. 7. In this diagram a circuit fragment is built from ten identical 12 Ω resistors. What is the resistance between the points labeled A and B? (a) 15 Ω (b) 25 Ω correct (c) 48 Ω (d) 72 Ω (e) 120 Ω 8. Two small spheres with equal masses m are suspended by strings of length 1 metre as shown. Both spheres have a net charge on them. Each string makes an angle of 30 o with the vertical in equilibrium. In equilibrium, which one of the following statements is true? V A C D Choose A, B, C or D. If none of them are right, choose E. If more than one are right then choose E too. Correct answer is C. (Look at the equipotential values. They rise to the peak so it s a positive charge concentration there, which attracts the negative charge.) 10. Three point charges are arranged as shown in the figure. The charges are now taken away to infinity, one by one, in the following order: first A, then B, and finally C. Calculate the work done by you in removing the charges one by one. W A is the work done in removing charge A, W B is the work done in removing charge B, and W C is the work done in removing charge C. Grid Spacing is one metre (a) Q 1 and Q 2 must have the same magnitudes. (b) Charges Q 1 and Q 2 must have opposite signs. correct (c) Q 1 must be a positive charge. (d) Both (a) and (b) (e) None of the above (a) W A = 0 J, W B = +1.5 10 3 J, W C = 0 J correct (b) W A = 0 J, W B = 1.5 10 3 J, W C = 0 J (c) W A = 3.6 10 3 J, W B = +1.5 10 3 J, W C = 0 J (d) W A = 3.6 10 3 J, W B = +1.5 10 3 J, W C = +3.6 10 3 J (e) W A = +3.6 10 3 J, W B = 1.5 10 3 J, W C = 3.6 10 3 J 3
There are two written problems. Show all your work and explain your reasoning to get full credit. 11. Three charges are arranged as shown in the figure. [10 pts] (a) Calculate the electric field due to charge A at the point X. E C E B E Tot E A Electric field of A is given by Grid Spacing is one metre E A = k c q A r 2 A where k c = 9 10 9 N-m 2 /C. r A = 2 m from the graph. Thus E A = 4500 N/C, down. (b) Draw vectors on the figure showing the electric fields due to A, B and C separately, approximately to scale. Show the total electric field vector as well. Label as needed. (c) Calculate the total electric field at point x due to the three charges A, B and C. Express as x and y components or in standard vector notation.. 3 E Ax = 0, E Bx = E Cx = k c q B = 576 N/C (3 2 + 2 2 ) 3/2 E x tot = 2 ( 576) = 1152 N/C E Ay = 4500 N/C,, E By = E Cxy E A tot = 4500 N/C 4
12. Analyse the the circuit shown. [10 pts] (a) Assume first that E = 0. Find the equivalent resistance of the 3-resistor circuit and calculate the current I 1. ( When E = 0 the middle battery is like a short.) I 1 68Ω I 3 100Ω E 150Ω 3V I 2 Note that E is considered replaced by a wire. So the 100-ohm resistor is in series with the parallel combo of 68-ohm and 150-ohm. R eq = 100 + 68 150 68 + 150 = 147Ω I 1 = 3 V/147Ω = 0.0204 A (b) Now assume E is not zero. Write the Kirchhoff loop equations that will allow solving for the three currents in terms of E. Node eqn: I 1 = I 2 + I 3 For 2 loop equations we have a choice. Since we re after I 1 start with two that contain I 1 : (c) Solve the equations for I 1 in terms of E. Get rid of I 2 in the first equation: I 2 = I 1 I 3 : 3 100I 1 68I 2 + E = 0 3 100I 1 150I 3 = 0 3 168I 1 + 68I 3 + E = 0 Reduce the second equation by 68/150 so it becomes: Now add the equations to get 1.36 45.3I 1 68I 3 = 0 4.36 213.3I 1 + E = 0 I 1 = 4.36 + E 213.3 = 0.0204 + E 213.3 A (d) In your result for the previous part, set E = 0 and compare the result to what you got in part (a). It is obviously the same: I 1 = 0.0204 A. 5