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Phys102Term: 152Second MajorSaturday, April 09, 2016Code: 20Page: 1Q1.Three point charges are arranged along the x-axis. Charge q 1 3 .0 0 μ C is at theorigin, and charge q 2 5 .0 0 μ C is at x 0.200 m. Where should a third chargeq 3 8 .0 0 μ C be located if the net force on q 1 is 7.00 N in the negative x-direction?A)B)C)D)E)Ans:– 0.144 m– 0.211 m 0.412 m 0.211 m– 0.520 m 5q2 3q1⃗Fnet 7 î⃗ 12 F⃗ 13 F⃗ 12 Fkq1 q 29 109 3 10 6 5 10 6 33.75 10 1 N24 10 2𝑟12⃗ 12 3.375 î (N)FTo the left of q1⃗ 13 F⃗ net F⃗ 12 7 î 3.375 î 10.375 î (N) F2r13 kq1 q 29 109 24 10 12 0.0208𝑚2 r13 0.144 mF1310.375Q2.Two identical small conducting spheres are separated by 0.6 m center to center. Thespheres carry different amounts of charge with a total charge of 4 μC. The twospheres are now connected by a very thin conducting wire and then disconnected. Thenew electric force on each sphere isA)B)C)D)E)0.1 N, repulsive0.1 N, attractive0.4 N, attractivezero0.4 N, repulsiveAns:The change of each sphere 2 μC Repulsive ForceF kq1 q 29 109 4 10 12 0.1 Nr20.36King Fahd University of Petroleum and MineralsPhysics Departmentc-20-n-20-s-0-e-1-fg-1-fo-0

Phys102Term: 152Q3.Second MajorSaturday, April 09, 2016Code: 20Page: 2An electric dipole consists of a charge of 1.0 C located at the point (0, 1.0) cm anda charge of – 1 µC located at the point (0, –1.0) cm. How much work must be done byan electric filed E 3 .0 1 0 ˆi (N/C) to align the dipole with the field?6A)B)C)D)E)Ans:0.060 J0.030 Jzero0.020 J0.12 J ⃗d ⃗P qdĵ 1.0 10 6 2.0 10 2 2.0 10 8 ĵ C m⃗U⃗ i p⃗ i ⃗E 0⃗U⃗ f p⃗ f ⃗E pE 2.0 10 8 3.0 106 0.06W U Ui Uf 0 0.06 0.06JJQ4.Charges of 3.0 μC are located at (0, 2.0) m and at (0, – 2.0) m, as shown in FIGURE1. Charges Q are located at (4.0, 2.0) m and at (4.0, – 2.0) m. The net electric field atthe origin is equal to 4 .0 1 0 ˆi (N/C). Determine Q.3A)B)C)D)E)Ans: 5.0 µC 3.1 µC 3.1 µC 6.4 µC 5.0 µCr 2 16 4 20 𝑟 4.47 𝑚Figure 1r θ The fields due to the 3μC charges cancel⃗ to be in the x direction, Q must be ( )For EE𝑛𝑒𝑡 2kQkQ 4kQ cosθ 2 2 2 32rrrrE r34 103 (4.47)3Q 4.969 μC8k8 9 109King Fahd University of Petroleum and MineralsPhysics Departmentc-20-n-20-s-0-e-1-fg-1-fo-0

Phys102Term: 152Second MajorSaturday, April 09, 2016Code: 20Page: 3Q5.FIGURE 2 shows two unequal point charges, q and Q, of opposite sign. Charge Qhas greater magnitude than charge q. In which of the regions X, Y, Z will there be apoint at which the net electric field due to these two charges is zero?Figure 2A)B)C)D)E)only region Xonly regions X and Zonly region Yonly region Zall three regionsqXQYZAns:AQ6.At each point on the surface of the cube shown in FIGURE 3, the electric field isparallel to the z axis. The length of each edge of the cube is 3.0 m. On the top face ofthe cube, the electric field is E 2 0 kˆ (N/C), and on the bottom face E 2 0 kˆ (N/C).Determine the net charge contained within the cube.Figure 3A)B)C)D)E)– 3.2 10-9 3.2 10-9– 1.9 10-10 1.9 10 -10 0.90 10-9CCCCCAns:Top:Φ𝑡 ⃗Ei ⃗Ai ( 20𝑘̂) (9.0 𝑘̂) 180Bottom:Nm2Φ𝑏 ⃗Eb ⃗Ab (20𝑘̂) ( 9.0 𝑘̂) 180CNm2CThere is no electric flux through the other sides.Φ𝑛𝑒𝑡Nm2 Φ𝑡 Φ𝑏 360CΦ𝑛𝑒𝑡 q 𝑒𝑛𝑐𝜀0 q 𝑒𝑛𝑐 𝜀0 Φ𝑛𝑒𝑡 8.85 10 12 ( 360) 3.19 10 9 CKing Fahd University of Petroleum and MineralsPhysics Departmentc-20-n-20-s-0-e-1-fg-1-fo-0

Phys102Term: 152Second MajorSaturday, April 09, 2016Code: 20Page: 4Q7.In FIGURE 4, short sections of two very long parallel lines of charge are shown,fixed in place, and separated by L 8.0 cm. The uniform linear charge densities are 6.0 μC/m for line 1 and – 2.0 μC/m for line 2. Where along the x-axis (from theorigin) is the net electric field due the two lines zero?Figure 4A) 8.0 cmB) 4.0 cmC) 2.0 cmD) 6.0 cmE) 0.0 cmAns:The point should be to the right of line z, at adistance (d) from it.𝐸1 𝐸2 :2𝑘𝜆1 2𝑘𝜆2 𝑑 𝐿𝑑𝑑 𝐿𝜆1𝐿6 1 3𝑑𝜆2𝑑2 𝐿𝐿 2 𝑑 4.0 cm𝑑2 𝑥 𝐿 𝑑 4 4 8 cm2Q8.An electron is shot directly toward the center of a large metal plate that has a surfacecharge density of – 2.0 C/m2. If the initial kinetic energy of the electron is 1.6 10-17J and if the electron is to stop (due to electrostatic repulsion from the plate) just as itreaches the plate, how far from the plate must the launch point of the electron be?A)B)C)D)E)0.44 mm3.3 mm25 mm14 mm6.4 mmAns: K UK i eV eEd e 𝜎 d𝜀0ε0 K i8.85 10 12 1.6 10 7 d 4.425 10 4 𝑚 0.44 𝑚𝑚eσ1.6 10 19 2 10 6King Fahd University of Petroleum and MineralsPhysics Departmentc-20-n-20-s-0-e-1-fg-1-fo-0

Phys102Term: 152Second MajorSaturday, April 09, 2016Code: 20Page: 5Q9.Charge Q is uniformly distributed in a sphere of radius R. Find the ratio of themagnitude of the electric field at r R/2 to that on the surface of the sphere. (r is thedistance from the center of the sphere)A)B)C)D)E)Ans:1/21/4241/3E𝑖𝑛 kq𝑘𝑞 𝑅1 𝑘𝑞𝑟 E𝑅/2 3 3𝑅𝑅 22 𝑅2E𝑠 𝑘𝑞𝑅2 E𝑅/2𝑘𝑞 𝑅 21 2E𝑠2𝑅 𝑘𝑞2Q10.An electron and a proton are accelerated from rest through the same potentialdifference. Which of the following statements is CORRECT?A)B)C)D)E)The electron has greater speed.The proton has greater speed.They have the same speed.The electron has greater kinetic energy.The proton has greater kinetic energy.Ans:K qVsamesame 12𝑞𝑉𝑚𝑣 2 𝑞𝑉 𝑣 2 𝑣 2𝑚2𝑞𝑉𝑚differentKing Fahd University of Petroleum and MineralsPhysics Departmentc-20-n-20-s-0-e-1-fg-1-fo-0

Phys102Term: 152Second MajorSaturday, April 09, 2016Code: 20Page: 6Q11.The electric potential at the surface of a conducting sphere is 200 V. At a point that is10.0 cm from the surface, the electric potential is 150 V. What is the radius of thesphere?A)B)C)D)E)Ans:30 cm33 cm25 cm14 cm28 cmkq𝑅 } v2 kq R Rkqv1R d kqR dV2 𝑅 𝑑V1 0.75 R R 0.75 R 0.75 dR d0.25 R 0.75 d R 3d 30 cmQ12.Two stationary point charges q1 2.0 nC and q2 – 2.0 nC are 0.10 m apart, asshown in FIGURE 5. Calculate the work done by the electric field on a charge of 2.0 nC that moves from point B to point A.Figure 5A)B)C)D)E) 0.15 J 0.15 J 1.1 J 1.1 JzeroAns:VA 0kq1 kq 29 109 2 10 9 9 109 2 10 9𝑉𝐵 𝑟1𝑟20.080.06VB 75 VW q V q(Vf Vi ) q (VA VB ) qVB 2.00 10 9 ( 75) 1.5 10 7King Fahd University of Petroleum and MineralsPhysics DepartmentJc-20-n-20-s-0-e-1-fg-1-fo-0

Phys102Term: 152Second MajorSaturday, April 09, 2016Code: 20Page: 7Q13.A particle with a charge of 5.0 nC is in a uniform electric field. It is released fromrest. Its kinetic energy is found to be 1.5 10-6 J after it has moved 5.0 cm. What isthe magnitude of the electric field?A)B)C)D)E)6.0 kV/m1.5 kV/m3.0 kV/m4.5 kV/m7.5 kV/m⃗E Ans:K qV qEdK1.5 10 6E 6.0 kV/mqd5.0 10 9 0.05Q14.The electric potential V (in volts) at points in the xyz space is given by:V xz2 y2z 4.0where x, y, and z are in meters. Find the electric field (in V/m) at the point (2.0, 4.0, 1.0) m.A) 1 .0 ˆi 8 .0 ˆj 2 0 kˆB) 2 .0 ˆi 3 .0 ˆj 1 .0 kˆC) 1 .0 ˆi 4 .0 ˆj 2 .0 kˆD) 4 .0 ˆi 1 4 ˆj 2 .0 kˆE) 5 .0 ˆi 3 .0 ˆj 6 .0 kˆAns:V xz 2 y 2 z 4Ex V ( z 2 ) z 2 1.0 V/m xEy V (2yz) 2yz ( 2)(4)( 1) 8.0 V/m yEz V ( 2xz 𝑦 2 ) 2xz 𝑦 2 (2)(2)( 1) 16 20 V/m zKing Fahd University of Petroleum and MineralsPhysics Departmentc-20-n-20-s-0-e-1-fg-1-fo-0

Phys102Term: 152Second MajorSaturday, April 09, 2016Code: 20Page: 8Q15.Two capacitors C1 and C2 are each charged to 60 V, and then disconnected from thebattery. They store charges of 100 μC and 300 μC. The two capacitors are thenconnected with opposite polarity as shown in FIGURE 7. What then is the potentialdifference across the capacitors?Figure 7A)B)C)D)E)Ans:C1 30 V120 V40 V20 V50 V100 5300520 𝜇𝐹; C2 5𝜇𝐹 𝐶1 𝐶2 5 6036033Series charge cancellation Redistribution ParallelQnet 200μCSame P. D.q1 C1 V} Qnet (C1 C2 )V V q 2 C2 VQnetC1 C2 20020 3 30 𝑉Q16.A charged isolated capacitor stores an energy of U. It is connected in parallel to anidentical uncharged capacitor. After the combination, the total energy stored in thetwo capacitors isA)B)C)D)E)Ans:Ui U/2UU/42U4Uq2 U q 2CU2CAfter:qfq2f111𝑈q1 CV C} Uf 𝑞2 2 𝐶𝑈 q 2 CVeq 2C2𝐶𝑒𝑞22𝐶4𝐶2King Fahd University of Petroleum and MineralsPhysics Departmentc-20-n-20-s-0-e-1-fg-1-fo-0

Phys102Term: 152Second MajorSaturday, April 09, 2016Code: 20Page: 9Q17.In the capacitor circuit shown in FIGURE 6, the capacitance of each capacitor is C.Find the ratio of Q3/Q2.Figure 6A)B)C)D)E)21/231/32/3Ans:V3 V Q3 CVQ1 Q 2 VCCQ2𝐶𝑉2 V Q2 C2Q32 𝐶𝑉 2Q2𝐶𝑉Q18.A 500-pF capacitor consists of two circular plates 15 cm in radius, separated by asheet of polystyrene ( 2.6). What is the thickness of the sheet?A)B)C)D)E)3.3 mm3.7 mm4.5 mm5.1 mm4.2 mmAns:C kCair d kε0 Adkε0 Akε0 π𝑟 22.6 8.85 10 12 𝜋 225 10 4 3.25 10 3 𝑚CC500 10 12King Fahd University of Petroleum and MineralsPhysics Departmentc-20-n-20-s-0-e-1-fg-1-fo-0

Phys102Term: 152Second MajorSaturday, April 09, 2016Code: 20Page: 10Q19.A light bulb has a tungsten filament and is powered by a battery. When the bulb isturned ON, its temperature is 20.0 oC and the current passing through it is 0.850 A.After 60.0 s, the current is 0.220 A. What then is the temperature of the filament?Tungsten has a temperature coefficient of resistivity of 4.50 10-3 (oC)-1. Assume thefilament’s dimensions did not change.A)B)C)D)E)Ans:R𝑖 656 oC561 oC415 oC280 oC300 oCVV; R𝑓 0.850.22R VIVV (1 4.5 10 3 𝑇)0.220.85 0.85 1 4.5 10 3 T T 636 0.22 T𝑓 656 Q20.Two points in a conducting wire are 75 cm apart and the potential difference betweenthem is 0.95 V. If the current density is 4.5 107 A/m2, what is the resistivity of thewire?A)B)C)D)E)Ans:2.8 10-8 .m1.5 10-8 .m1.7 10-8 .m2.4 10-8 .m5.3 10-8 .mE ρJV0.95𝑉} ρ 2.8 10 8 Ω m7𝑑𝐽0.75 4.5 10 ρJ𝑑King Fahd University of Petroleum and MineralsPhysics Departmentc-20-n-20-s-0-e-1-fg-1-fo-0

Phys102 Second Major Code: 20 Term: 152 Saturday, April 09, 2016 Page: 1 King Fahd University of Petroleum and Minerals Physics Department c-20-n-20-s-0-e-1-fg-1-fo-0