# Department of Physics. PHYS MAJOR 2 EXAM Test Code: 015. Monday 1 st May 2006 Exam Duration: 2hrs (from 6:30pm to 8:30pm)

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1 Department of Physics PHYS1005 MJOR EXM Test Code: 015 Monday 1 st May 006 Exam Duration: hrs (from 6:30pm to 8:30pm) Name: Student Number: Section Number: Version 15 Page 1

2 1. Each of the four capacitors shown in figure 5 is 500 µf. The voltmeter reads 1000V. The magnitude of the charge, on each capacitor plate is: ) 3.5 C B) 0. C C) 0.5 C D) 5.5 C E). C. particle with a charge of 5.5 x 10 8 C is fixed at the origin. How much work is done by external agent to move a charge of.3 x 10 8 C from point to point B shown in figure 6. ) 3.1 x 10 3 J B) 6.0 x 10 5 J C) zero D) 6.0 x 10 5 J E) 3.1 x 10 3 J 3. parallelplate capacitor has a plate area of 0. m and a plate separation of 0.1mm. The electric field between the plates is V/m. The energy stored in the capacitor is: ) 4.36 mj B).76 mj C) 1.54 mj D) 0.15 mj E) 0.35 mj 4. charged particle with a mass of x10 4 kg is held suspended (stationary) by a downward electric field of 300 N/C. The charge on the particle is: ) 1.5 x 10 6 C B) 1.5 x 10 6 C C) 6.5 x 10 6 C D) 4.0 x 10 6 C E) 6.5 x 10 6 C Version 15 Page

3 5. Consider the charges shown in figure 1. Find the magnitude and sign of charge Q 4 so that the net electrostatic force on charge Q 5 is zero. ) 0.9 nc B).5 nc C).5 nc D) 1.8 nc E) 1.8 nc 6. n airfilled parallelplate capacitor has a capacitance of 1 pf. The plate separation is then doubled and a wax dielectric is inserted, completely filling the space between the plates. s a result, the capacitance becomes pf. The dielectric constant of the wax is: ) 0.4 B) 4.0 C) 8.0 D).0 E) long solid nonconducting cylinder (radius = 1 cm) has a uniform charge density (5.0 nc/m 3 ) distributed throughout its volume. Determine the magnitude of the electric field 5.0 cm from the axis of the cylinder. ) 5 N/C B) 14 N/C C) 31 N/C D) 5 N/C E) 0 N/C 8. large insulating solid sphere has a charge density of 5 nc/m 3. Calculate the electric field inside the sphere at a distance of 10 cm from its center. ) 1.6 N/C B) 0 C) 6.4 N/C D) 18.8 N/C E) 5.50 N/C 9. In figure, two charges q 1 = 5.0 µc, q = 10 µc, are fixed on the xaxis. t what distance, measured from q 1, the electric field will be zero? ).4 m to the left of q 1 B) 1.5 m to the left of q 1 C) 0.5 m to the left of q 1 D) 3.5 m to the left of q 1 E) 0.5 m to the right of q 1 Version 15 Page 3

4 10. Which of the following charge CNNOT be found in nature? ) 4.8 x10 19 C B) 64 x10 19 C C) 16 x10 19 C D) 0.8 x10 19 C E) 3. x10 19 C 11. Two conducting spheres, one having twice the diameter of the other, are separated by a distance large compared to their diameters. The smaller sphere has charge q and the larger sphere is uncharged. If the spheres are connected by a long thin conducting wire: ) 1 and have the same charge B) The value of the electric field at both surfaces is same C) 1 and have the same potential D) has half the potential as 1 E) has twice the potential as 1 1. Two small identical conducting spheres, initially uncharged are separated by a distance of 1.0 m. Find the number of electrons that must be transferred from one sphere to the other in order to produce an attractive force of x10 4 N between the spheres. ) 1.6 x B).4 x C) 9.3 x D).1 x E) 3.5 x Two electrons are initially far away. Each electron is moving toward the other one with a speed of 500 m/s. Find the closest distance they can get to each other. ) 4.14 mm B) 0.67 mm C) 1.53 mm D) 1.01 mm E) 9.11 mm 14. Three large insulating sheets of charge with the given charge densities are shown in figure 4. The magnitudes of electric field at points and B are respectively ) 3σ o / ε o, 3σ o / ε o B) σ o / ε o, 0 C) σ o / ε o, σ o / ε o D) 3σ o / ε o, 0 E) σ o / ε o, 0 Version 15 Page 4

5 15. conducting spherical shell with a net charge q o has an outer radius R. point charge q o is placed at a distance R/3 from the center of the shell. What is the surface charge density on the outer surface of the shell? ) q o / 4π R B) q o / 4π R C) 0 D) q o / 4π R E) q o / 4π R 16. In a certain region of the xy plane, the electric potential is given by V (x,y) = xy 3x 5y, where t which point is the electric field equal to zero? ) (7.5, 3.5) B) (.5, 7.5) C) (3.5, 8.5) D) ( 3.5,.5) E) (7.5,.5) 17. Capacitors and B have the same capacitance. Capacitor is charged so that it stores 4 J of energy and capacitor B is uncharged. The capacitors are then connected in parallel. The total stored energy in the capacitors is now: ) 1 J B) 4 J C) 14 J D) 8 J E) J 18. charged solid conducting sphere has a radius = 0 cm and a potential of 400V. Calculate the electric field 40 cm from the center of the sphere, ) 50 V/m B) 750 V/m C) 500 V/m D) 100 V/m E) 400 V/m Version 15 Page 5

6 19. Two large metal plates are 10.0 cm apart and have a uniform electric field between them as shown in figure 3. n electron is released from rest from the negative plate at the same time a proton is released from rest from the positive plate. Find the ratio of the distance covered by proton to that of electron when they pass each other. ) 5.46 x 10 4 B) 7.87 x 10 4 C) 9.43 x 10 4 D) 1.09 x 10 4 E) 3.3 x Consider a long wire of linear charge density λ. Now imagine a closed cylindrical Gaussian surface of radius r and length L with the wire as the axis. What is the electric flux through the cylinder surface? ) (πr /L L) λ/ε o B) λl/ε o C) 0 D) (λ L / π r ) λ E) (πr L) λ/ε o Version 15 Page 6

7 nswer Key 1. C. D 3. E 4. C 5. E 6. B 7. B 8. D D 11. C 1. C 13. D 14. C 15. D 16. B 17. E 18. C B Version 15 Page 7

8 Q 3 = 5 nc 5 cm Q 1 = nc Q 5 = 3 nc 4 cm 4 cm 3 cm Q = nc q 1 1m q FIGURE x FIGURE 1 Q 4 e p σ o B σ o σ o 10 cm FIGURE 3 FIGURE 4 v B 4.3 cm Q = cm FIGURE 5 FIGURE 6 Version 15 Page 8

9 Physics 10 Formula Sheet for nd Major Exam Second Semester (Term 05) q1q F = k, Φ =, r E.d Surface q q E = k, E = k r, 3 r R U = P. E, τ = P E, Φ c E x qin = E. d = ε V V =, E y =, x y V = V B V 0 = B σ E = ε kλ E =, r K = U E z U E.dS = q 0 V = z o σ E = ε q q1q V = k, U = k, W app = q V= U r r 1 o v = v o at 1 x x o = vot a t v = v o a (xx o ) Constants: k = N.m /C ε 0 = C /N.m e = C m e = kg m p = kg k B = J/K N = molecules/mole R = J/mol. K 1 atm = N/m g = 9.8 m/s micro = 10 6 nano = 10 9 pico = 10 1 q 1 C =, C = κ C0, U = CV V dq i =, V = ir, P dt i J =, J = ( ne) vd, E = = iv ρ J L R = ρ, ρ ρo = αρ o( T T o ) Version 15 Page 9

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