Phys10 Secon Major-1 Zero Version Coorinator: Sunaii Sunay, April 1, 013 Page: 1 Q1. Two ientical conucting spheres A an B carry eual charge Q, an are separate by a istance much larger than their iameters. Initially the electrostatic force between them is F. A thir ientical uncharge conucting sphere C is first touche to A, then to B, an then move away. As a result of this, the electrostatic force between A an B becomes: A) 3F/8 B) F/4 C) F/ D) F/16 E) F The charge on A will be Q The charge on B will be 3 4 Q F = k a 3 4 Q r = 3 8 k Q r = 3 8 F Q. A positively charge sphere of mass 1.00 g falls from rest from a height of 5.00 m, in a uniform electric fiel of magnitue 1.00 10 4 N/C an is irecte vertically ownwar. The sphere hits the groun with a spee of 0.0 m/s. What is the charge on the sphere? A) + 3.0 µc B) 1.00 µc C) + 5.3 µc D) 5.3 µc E) + 1.00 µc v f = v o + ay a = v f = 40 m/s y ma mg F = ma = mg + E = = 3.0 10 6 C E c-0-n-0-s-0-e-1-fg-1-fo-0
Phys10 Secon Major-1 Zero Version Coorinator: Sunaii Sunay, April 1, 013 Page: Q3. Figure 1 shows a ipole rotating uner the effect of an electric fiel pointing along the negative x-axis. Which one of the following statements is TRUE Figure 1 E + - A) The potential energy of the ipole is ecreasing. B) The torue on the ipole is irecte into of the page. C) The ipole is rotating clockwise. D) The work one on the ipole by the fiel is negative. E) The ipole will stop when it is pointing parallel to the positive x-axis. Q4. A Three point charges are locate at the corners of a suare as shown in Figure. Fin the value of Q if the electric fiel at the corner A is zero. Take = 7.00 µc A) 19.8 µc B) 14.0 µc C) 9.90 µc D) 4.95 µc E).54 µc Figure A E E Q 45 At A : Q E Q is positive E Q cos45 0 = E k Q ( + ) cos45 = k Q Q cos450 = Q = 19.8 µc c-0-n-0-s-0-e-1-fg-1-fo-0
Phys10 Secon Major-1 Zero Version Coorinator: Sunaii Sunay, April 1, 013 Page: 3 Q5. Figure 3 a, b an c, show the cross sections of three cyliners each carrying a uniform charge Q. Concentric with each cyliner is a cylinrical Gaussian surface, all three with the same raius. Rank the Gaussian surfaces accoring to the electric fiel at any point on the surface, GREATEST FIRST. Figure 3 Cyliner Gaussian surface (a) (b) (c) Q6. A) All tie B) a, b, c C) b, c, a D) c, b, a E) a, c, b A uniformly charge conucting sphere of 3.0 cm iameter has a surface charge ensity of 10 μc/m. Fin the total electric flux leaving the surface of the sphere. A) 3. 10 3 N.m /C B) 1.3 10 4 N.m /C C).5 10 3 N.m /C 5 D) 1.4 10 N.m /C E) 6.7 10 N.m /C ϕ = ε 0 = σa ε 0 = σ(4πr ) ε 0 = 3. 10 3 Nm /C c-0-n-0-s-0-e-1-fg-1-fo-0
Phys10 Secon Major-1 Zero Version Coorinator: Sunaii Sunay, April 1, 013 Page: 4 Q7. A 6.0 µc charge is place on a thin spherical conucting shell of raius R = 5.0 cm. A particle with a charge of 10 µc is place at the center of the shell. The magnitue an irection of the electric fiel at a point R from the center of the shell are: E = A) 3.6 10 6 N/C, towar the center 6 B) 3.6 10 N/C, away from the center C) 0 D) 5.4 10 6 N/C, towar the center E) 5.4 10 6 N/C, away from the center k(6.0μc 10μC) (R) = 3.6 10 6 N/C Q8. A long, straight wire has fixe negative charge with a linear charge ensity of magnitue 4.5 nc/m. The wire is enclose by a coaxial, thin walle nonconucting cylinrical shell of raius 0 cm. The shell is to have a positive charge on its outsie surface (with a surface charge ensity σ) that makes the net electric fiel at points 30 cm from the center of the shell eual to zero. Calculate σ. E = A) 3.6 10 9 C/m B) 3.0 10 10 C/m 10 C) 1.5 10 C/m 7 D) 4.5 10 C/m 5 E) 7.8 10 C/m λ 1 πε 0 r + λ πε 0 r = 0 λ 1 = λ = l = σa l = σπrl l σ = λ 1 4.5 10 9 = πr π(0.) = 3.6 10 9 C c-0-n-0-s-0-e-1-fg-1-fo-0
Phys10 Secon Major-1 Zero Version Coorinator: Sunaii Sunay, April 1, 013 Page: 5 Q9. Two large metal plates of area.0 m face each other, 6.0 cm apart, with eual charge magnitues but opposite signs. The magnitue of the electric fiel between the plates is 1. 10 N/C. Fin. A).1 nc B) 1.1 nc C) 0.50 nc D) 13 nc E) 0.40 nc E = σ ε 0 = Aε 0 = E(Aε 0 ) =.1 nc Q10. A glass sphere of iameter 1.00 mm has been charge to + 100 nc. A proton is fire from a large istance towar the sphere. What initial spee must the proton have to just reach the surface of the sphere? (Take V=0 at a large istance from the sphere) A) 1.86 10 7 m/s 7 B) 9.10 10 m/s 6 C) 5.34 10 m/s 9 D) 4.50 10 m/s E).67 10 6 m/s 1 mv = ev = e k r v = m e k r (e is teh change of the electron) c-0-n-0-s-0-e-1-fg-1-fo-0
Phys10 Secon Major-1 Zero Version Coorinator: Sunaii Sunay, April 1, 013 Page: 6 Q11. Figure 4 shows a plot for the electric fiel E x as a function of x. Fin the magnitue of the potential ifference between the points x =.00 m an x = 6.00 m. Figure 4 8 Ex ( V/m) 6 4 0 1 3 4 5 6 7 X (m) Q1. A) 14.5 V B) 1.5 V C) 10.0 V D) 16.5 V E) 11.0 V Area uner the curve betwen x = an x = 6 m What are the magnitue an irection of the electric fiel at point P in Figure 5? Figure 5 A) 1.0 10 4 V/m to the left 4 B) 1.0 10 V/m to the right 4 C).0 10 V/m to the left 4 D).0 10 V/m to the right E) 3.0 10 3 V/m upwar P 1 cm 0.5 cm 0.5 cm E = V x = V x = 100 1 cm 0 V 100 V 00 V = 10000 V/m c-0-n-0-s-0-e-1-fg-1-fo-0
Phys10 Secon Major-1 Zero Version Coorinator: Sunaii Sunay, April 1, 013 Page: 7 Q13. What is the charge on a conucting sphere of raius R = 0.0 m if the potential at a istance r = 0.10 m from the center of the sphere is 1500 V. (Take V = 0 at infinity). A) 3.3 10 8 C 8 B) 1.7 10 C 8 C) 1.5 10 C 8 D).5 10 C E) 4.5 10 8 C V = k Q R Q = RV k Q14. In Figure 6, particles with charges 1 = + 10 µc an = 30 µc are fixe in place with a separation of = 4 cm. What is the value of Q that will make the potential eual zero at point P. Figure 6 A) 7.1 µc B) 5.1 µc C) 10 µc D) 3.5 µc E) 4.5 µc P Q 1 V = 0 = h 1 + h + h Q = 1 Q 30 = 10 = 7.1µC c-0-n-0-s-0-e-1-fg-1-fo-0
Phys10 Secon Major-1 Zero Version Coorinator: Sunaii Sunay, April 1, 013 Page: 8 Q15. Figure 7 shows three circuits, each consisting of a switch S an two capacitors, initially charge as inicate (top plate positive). After the switches have been close, rank the charge on the right capacitor, GREATEST FIRST. Figure 7 S S S 3 9 3 9 3 9 C C C 4C 3C 3C (1) () (3) A A) 1 an tie, then 3 B), 1, 3 C) All tie D) 3,, 1 E) 3, 1, Q16. Two capacitors are ientical except that one is fille with air an the other is fille with oil. Both capacitors carry the same charge. If E air refers to the electric fiel insie the capacitor fille with air, an E oil refers to the electric fiel insie the capacitor fille with oil, then the ratio of the electric fiels E air /E oil will be: E air E oil = κ oil κ air A) greater than 1 B) less than 1 C) 0 D) 1 E) None of the other answers c-0-n-0-s-0-e-1-fg-1-fo-0
Phys10 Secon Major-1 Zero Version Coorinator: Sunaii Sunay, April 1, 013 Page: 9 Q17. Three ientical capacitors are shown in Figure 8. A potential ifference V = 10 kv is establishe when the switch S is close. Fin the value of the capacitance C if the charge that passes through the meter M is 0.0 C. A) 6.7 µf B) 0 µf C) 1.6 µf D) 13 µf E).5 µf S M Figure 8 C e = 3C 3C = V V C C C = 10 5 F C = 6.7 10 6 F Q18. Consier the circuit of ientical capacitors shown in Figure 9. A potential ifference of.0 10 V is applie by the battery V. Calculate the energy store in the system if the capacitance of each capacitor is 50 µf. A) 3.0 J B) 4.0 J C) 6.0 J D) 1.0 J E) 7.0 J Figure 9 Take one branch C e = C + C = 3 C - + V E = 1 C ev For the whole circuit E = 1 C ev = 3.0 J c-0-n-0-s-0-e-1-fg-1-fo-0
Phys10 Secon Major-1 Zero Version Coorinator: Sunaii Sunay, April 1, 013 Page: 10 Q19. A cylinrical resistor of raius.5 mm an length 4.0 cm is mae of a material that has a resistivity of 3.5 10 5 Ω. m. What is the potential ifference when the energy issipation rate in the resistor is 1.0 W? A) 0.7 V B) 1.8 V C). V D) 0.17 V E) 1.1 V R = ρ L A = 0.071 Ω P = 1.0 = V R V = R = 0.7 V Q0. A 1.0-m-long wire has a resistance eual to 0.30 Ω. A secon wire mae of ientical material has a length of.0 m an a mass eual to the mass of the first wire. What is the resistance of the secon wire? A) 1. Ω B) 1.0 Ω C) 3.4 Ω D) 4.3 Ω E) 5.6 Ω R 1 = ρ L 1 A 1, R = ρ L A, ensity = m V = m AL A = V L R R 1 = L L 1 A 1 A = L L 1 = L = 4 L 1 R = 4R 1 = 1. Ω V L L 1 V c-0-n-0-s-0-e-1-fg-1-fo-0
F = k r U 1 = -p E τ = p E Φ = Surface E. A in Φ c = E. A = ε 0 σ E = ε o E = σ ε o E = k r E = k r 3 R kλ E = r B V = V - V = - E. S = V = k r B A A U 0 C = V C = κc air 1 U = CV 1 U = ε E I = o I = JA Q t V L R = = ρ I A J = σ E ρ = ρ [1 + α( T - T )] 0 0 P = IV ------------------------------------------------------ v = v o + at 1 x - x o = v ot + a t v = v o + a (x-x o ) Constants: E U x V V =, Ey =, Ez x y 1 = k r 1 V = z k = 9.00 10 9 N.m /C ε0 = 8.85 10-1 C /N.m e = 1.60 10-19 C me = 9.11 10-31 kg mp = 1.67 10-7 kg g = 9.8 m/s µ = micro = 10 n = nano = 10 p = pico = 10-6 -9-1