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1 Phys 2B Final Exam Name: Multiple Choice (3 points each) 1. Two capacitors initially uncharged are connected in series to a battery, as shown. What is the charge on the top plate of C 1? a. 81 μc b. 18 μc c. 0 μc d μc e μc 2. Two charges are located on the x axis of a coordinate system as shown. The charge +2q is located at x = +3a and the charge +q is located at x = 3a. Where on the x axis should an additional charge +4q be located to produce an electric field equal to zero at the origin O? a. x = 6 a b. x = 2 a c. x = + a d. x = + 2 a e. x = + 6 a 3. A proton p and an electron e are released simultaneously on opposite sides of an evacuated area between large, uniformly charged parallel plates, as shown above. Each particle is accelerated toward the oppositely charged plate. The particles are far enough apart so that they do not affect each other. Which particle has the greater kinetic energy upon reaching the oppositely charged plate? a. The electron b. The proton c. neither particle; both kinetic energies are the same. d. It cannot be determined without knowing the value of the potential difference between the plates. e. It cannot be determined without knowing the amount of charge on the plates. 4. Wire of resistivity ρ and cross sectional area A is formed into an equilateral triangle of side b, as shown. The equivalent resistance between two vertices of the triangle, X and Y, is (hint: consider two resistors in parallel) a. 3 A/(2ρb) b. 3 A/(ρb) c. 2 ρb/(3a) d. 3 ρb/(2a) e. 3 ρb/(a)

2 5. A right angled construction frame ABC, when measured at rest, has dimensions as follows: AB = m, AC = m, and BC = m. The frame is given a velocity of 0.59c, relative to the space platform, in a direction parallel to AC. The dimensions of the moving frame are measured simultaneously by observers on the platform. In the figure, the length AB measured by these observers is closest to: (hint: Pythagorean Theorem + Length contraction) a b c d e What type of mirror produces a real image of magnification M = 4 when an object is located 10 cm in front of it? a. a convex mirror of radius 4 cm b. a concave mirror of radius 4 cm c. a convex mirror of radius 16 cm d. a concave mirror of radius 16 cm e. none of the above 7. What is the spacing between adjacent bright interference fringes when a pair of slits 0.1 mm apart are illuminated by light of wavelength 500 nm, and the fringes are observed on a screen 2 m behind the slits? a. 0.5 cm b. 1.0 cm c. 2.0 cm d cm e. none of these 8. Light has wavelength 600 nm in a vacuum. It passes into glass, which has an index of refraction of What is the frequency of the light inside the glass? a. 3.3*10 14 Hz b. 5.0*10 14 Hz c. 3.3*10 5 Hz d. 5.0*10 5 Hz 9. One beam of coherent light travels path P 1 in arriving at point Q and another coherent beam travels path P 2 in arriving at the same point. If these two beams are to interfere destructively, the path difference P 1 P 2 must be equal to a. an odd number of half wavelengths. b. zero. c. a whole number of wavelengths. d. a whole number of half wavelengths.

3 10. A vertical wire carries an electric current into the page. What is the direction of the magnetic field at point P located to the south from the wire? a. West. b. North c. East d. South. e. Down. 11. Which of the following statements about conductors under electrostatic conditions is true? a. Positive work is required to move a positive charge over the surface of a conductor b. Charge that is placed on the surface of a conductor always spreads evenly over the surface. c. The electric potential inside a conductor is always zero. d. The electric field at the surface of a conductor is tangent to the surface. e. The electric field at the surface of a conductor is perpendicular to the surface. 12. A charge of 0.80 nc is placed at the center of a cube that measures 4.0 m along each edge. What is the electric flux through one face of the cube? a. 90 Nm 2 /C b. 15 Nm 2 /C c. 45 Nm 2 /C d. 23 Nm 2 /C e. 64 Nm 2 /C

4 13. (20 Points) Two point charges are fixed at the coordinates shown in the diagram. a. Calculate the magnitudes of the x and y components of the net electric field at the origin (0,0). b. Draw on the picture a vector for the net electric field. c. Calculate the electric potential at the origin. d. How much work would be required to bring a 3rd charge of q 3 = nc from very far away to the origin? e. Calculate the magnitude of the net force on q 3 due to the other two charges when it is at the origin.

5 14. (20 Points) A thin film of transparent oil is placed on top of a transparent plate. The oil film is then illuminated by white light shining onto the oil s surface, as shown in the figure above. To an observer standing right next to the light source and looking straight down on the oil film, the oil film appears green, corresponding to wavelength of 520 nm in air. The oil has an index of refraction of a. What is the frequency of the light in air? in the oil? b. If n plate > n oil, what is the minimum thickness that would cause the light to be green (constructive interference). c. What is the next smallest thickness that would also lead to the observer seeing green? d. If n plate < n oil, what is the minimum thickness that would cause the light to be green (constructive interference).

6 15. (20 points) Four lightbulbs are connected in a circuit with a 24 V battery as shown. a. Determine the average potential energy change of an electron as it moves from point Z to point X. Indicate whether it gains or loses potential energy in moving from Z to X. b. Calculate the equivalent resistance of the circuit. c. Calculate the magnitude of the current through point Y. d. Calculate the power dissipated by the 12 Ω bulb. e. Rank the bulbs in order of brightness (Hint: Brightness is related to power output.).

7 16. (20 pts) A coil in the shape of a rectangle, 0.25 m by 0.15 m, has a resistance of 5.0 Ω. In position 1 shown, the loop is in a uniform magnetic field B of 0.20 T. The field is directed out of the page, perpendicular to the plane of the loop. The loop is pulled to the right at a constant velocity, reaching position 2 in 0.50 s, where B is equal to zero. a. Calculate the average emf induced in the coil during this period. b. Calculate the magnitude of the current induced in the coil and state its direction. c. Calculate the power dissipated in the coil. d. Given that the coil moves a distance of 0.25 m, calculate the magnitude of the average force necessary to remove coil from the magnetic field. (use P ower = F avg v ) e. Calculate the average force on the left piece of the coil due to the interaction of the induced current with the magnetic field. Compare this to what you found in part d. Explain why they are the same or different.

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