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Physics 196 Spring 2013 Exam 1 Time Allowed: two hours Some Physics Constants: Name: e = 1.6×10-19 C k = 9.0×109 Nm2/C2 electronic charge Coulomb constant Permittivity of free space Mass of electron Mass of proton Avogadro’s number e0 = 8.85´10-12 C 2 / N × m2 me = 9.11×10-31 kg mp = 1.67×10-27 kg NA= 6.02×1023 PART A (48 points) The next 12 questions are worth 4 points each. Show work for problems with numerical answers. 1. The symbol of a chromium isotope is 24 Cr 52 . For the ion Cr +++ of this isotope, supply the missing information in the following sentences (a) (b) (c) (d) The number of protons is The number of neutrons is The number of electrons is The charge of the ion in C is 2. All electrons are removed from a 20-g sample of pure chromium. What is the charge on the sample? (a) (b) (c) (d) 4.42 ´105 C 4.42 ´103 C 8.84 ´105 C 8.84 ´103 C 3. The following diagrams describe a sequence of events during which a negatively charged rod is brought close to two neutral metal spheres in contact with each other, one sphere is then grounded, the spheres are then separated, and the charged rod is then moved away. Indicate with the symbols + or - the sign of the charge on each sphere in each step. 1 4. A,B, and C are three identical metal spheres carrying charges +8mC , -12mC and +4mC respectively. A and B are first brought together and then separated. Afterwards, B and C are brought together and separated. What is now the charge on B? (a) (b) (c) (d) 4mC 3mC 2mC 1mC 5. Electric force exists between two point charges at a certain distance apart. Under which of the following circumstances would the force be doubled? (more than one answer possible) (a) the distance is halved (b) the distance shrinks to 1 2 of the original value (c) both charges are doubled, and the distance is also doubled (d) one charge becomes eight times as much, and the distance is doubled 6. Since the force F experienced by a small charge q placed in a location where the electric field is E obeys the equation E = F q , it can be concluded that when the charge is replaced by a stronger charge, (a) (b) (b) (c) the electric field will increase the electric field will be reduced the force will increase the force will decrease 7. A point charge of -2.4nC at a certain location is found to experience a force of 6.7µN pointing East due to the electric charges in the surrounding. What is the direction and magnitude of the electric field at that location? (a) 640 N/C due East (b) 640 N/C due West (c) 2800 N/C due East (d) 2800 N/C due West 2 8. The diagram below shows four point charges at the corners of a square. Together, they produce an electric field at the center of the square pointing straight down. Three of the charges have the values indicated. What is the charge on the fourth one? (a) (b) (c) (d) -2C +2C -4C +4C 9. Sketch 10 electric field lines for the three point charges as shown that reflect the relative strength of the charges. 3 10. Refer the figure showing infinite sheet charges with surface charge densities –3σ and σ respectively. The x-component of the electric field at the point P is (a) s e0 (b) s e0 (c) 2s e0 (d) 2s e0 to the right to the left to the right to the left 11. A 90-degree arc of a circle of radius R carries total charge q uniformly distributed on its length. A small line segment subtending the angle dq at the center is shown. Find the y-component of the electric field produced by this segment at the center. 2kq sinq dq R2 2kq (b) 2 cosq dq R 2kq (c) sinq dq p R2 2kq (d) cosq dq p R2 (a) - 12. Describe in one or two sentences the defining property of an electric field line. 4 PART B (52 points) 13. The diagram below shows two point charges A and B on the x-y plane. The charge on A is -3nC and its coordinates are (-2,0). The charge on B is +12nC and the coordinates of B is (2,0). Coordinates are measured in meters. (a) (5 points) Find the magnitude and direction of the electric field at the point (-1,0). (b) (5 points) Find the x-coordinate of a point on the x-axis where the electric field vanishes. (c) (5 points) Sketch below the x-component of the electric field for points on the x-axis as a function of the xcoordinate of the points. (That is, the function Ex ( x ) ) 5 (d) (6 points) Determine the electric field at the point (-2,3) in the component form E = Exiˆ + Ey ĵ (Correct to two decimal places) (e) (4 points) If a rod connects the point charges A and B, does it experience compressive or tensile force? What is the magnitude of the force? 14. The diagram shows two charged sheets carrying total charges of equal magnitude but opposite signs, creating a uniform electric field of 5, 000 N C pointing upward. The sheets are 5.0cm apart. (a) (4 points) A proton is placed just above the bottom sheet with zero velocity. Find its velocity when it reaches the top sheet, ignoring gravity. 6 (b) (4 points) Another proton is placed just above the bottom sheet but with a horizontal velocity of 1.40 ´10 5 m / s , find the horizontal distance travelled by the proton when it reaches the top sheet, ignoring gravity. (c) (3 points) In the scenario of (b), find the angle between the velocity vector and the horizontal when the proton reaches the upper sheet, ignoring gravity. (d) (4 points) A small object of mass 6.0g carrying charge of +50.0mC is placed at the bottom sheet with zero velocity. Find how long it takes to reach the top sheet. (Can gravity be ignored?) 7 15. A thin rod of length 2m occupies the portion of x-axis from x = -2.0m to +2.0m . It carries electric charge so that the linear charge density is given by the function l ( x ) = Ax , where A is a constant. (a) (4 points) Find (a) the total charge and (b) the charge between the points x = 0 and x = 2m on the rod. (b) (4 points) Find the x-component of the electric field at the point x = 3.0m . Express your result in terms of k and q , where q is the charge between the points x = 0 and x = 2m . (c) (4 points) Find the x-component of the electric field at the point x = -3.0m . Express your result in terms of k and q , where q is the charge between the points x = 0 and x = 2m . (Hint: use the result in (b)) 8