1 pt What is the total charge of the thorium nucleus? (The neutral thorium atom has 90 electrons.) (in C) 1. A B 1.

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1 Keep this exam CLOSED until advised by the instructor. 120 minute long closed book exam. Fill out the bubble sheet: last name, first initial, student number. Leave the section, code, form and signature areas empty. Four single sided (or two double sided) handwritten 8.5 by 11 help sheets are allowed. When done, hand in your test and your bubble sheet. Thank you and good luck! Posssibly useful constants: k = Nm 2 /C 2 ǫ 0 = As/(Vm) µ 0 = 4π 10-7 Vs/(Am) = Vs/(Am) What is the total charge of the thorium nucleus? (The neutral thorium atom has 90 electrons.) (in C) 1. A B C E G D F H What is the magnitude of its electric field at a distance of m from the nucleus? (in N/C) 2. A B C D E F G H c = 299,792,458 m/s e = C m e = kg E e = 511 kev 1 ev = J

2 What is the magnitude of the force on an electron at that distance? (in N) 3. A B C D E F G H ) 1.44E-17 [1.4112e e-17] Unit: C 2) 3) 5.20E+11 [ ] Unit: N/C F 8.32E-08 [ e e-08] Unit: N What is the magnitude of the electric field at point B? (in N/C) 5. A B C D E F G H What is the electric potential at point A? (in V) 6. A 0.00 B C D E F G H What is the electric potential at point B? (in V) 7. A B C D E F G H ) 0.00 Unit: N/C Two equal point charges Q = 4.99 µc are separated by a distance d = 2.00 m. (See figure.) Q A Q Point A is halfway between the charges and point B is located 1.00 m to the right of the second charge. What is the magnitude of the electric field at point A? (in N/C) 4. A 0.00 B C D E F B G H ) 6) 7) 4.98E+04 [ ] Unit: N/C 8.97E+04 [ ] Unit: V 5.98E+04 [ ] Unit: V

3 A capacitor is charged to 1 coulomb; the capacitance is farads. Then a switch is closed which puts the capacitor in a closed circuit with a resistor; the resistance is ohms. Calculate the charge on the capacitor after 7.00 milliseconds. (1 ms = s) (in C) 8. A B C ) D E F G H E [ ] Sig 3-6 Unit: C Calculate the average induced voltage between the tips of the wings of a Boeing 767 flying at 290 km/h above Golden, Colorado. The downward component of the earth s magnetic field at this place is T. (Assume that the wingspan is 60 m.) (in V) 9. A B C D E F G H ǫ mf = Blv where l = wing span and v = velocity. 9) 3.38E-01 [ ] Unit: V The figure shows the equipotential lines of a charge distribution and labelled locations. D B C Where do you expect the strongest electric field? 10. A A B B C C D D E E What is the direction of the electric field at E? 11. A Approximately parallel to the x-axis. B Approximately parallel to the y-axis. C No field. What is the direction of the electric field at C? 12. A Approximately parallel to the x-axis. B Approximately parallel to the y-axis. C No field. 10) 11) 12) true true true A E

4 In the section of circuit below, R Ω, R Ω, and R Ω. Find the equivalent resistance of this combination of resistors. R 2 R 3 a. b. R 1 (in Ohm) 13. A B C ) D E 1.17 F 1.55 G 2.06 H E-01 [ ] Unit: Ohm What is the equivalent capacitance between points A and B in the following circuit where, C 1 = 30 µf, C 2 = 22 µf, C 3 = 10 µf, Two wires run parallel to each other with currents I 1 = A, and I 2 = 56.5 A. If they are a = 0.02 m apart, what is the magnitude of the force (N) per meter of length? Hint: See: "Two Wires." Answer: F/L = µ 0 I 1 I 2 / (2π r) Here we just need the magnitude, so: F/L = µ A 56.5 A / (2π 0.02 m) F/L = N/m Give your answer to at least three significant figures. Your answer must be accurate to 1%. 14. A B C D E F G H µf 14) E [ ] Sig 2-15

5 In the circuit below R 1 = 96, R 2 = 55, R 3 = 127 Ω, and V = 70 V. What is the power dissipated (in W) in the R 1 resistor? In the diagrams below, the solid arrow represents the object and the dashed arrow the image. The rectangle shows the position of a SINGLE OPTICAL ELEMENT. Match each diagram with the appropriate optical element. 15. A Plane Mirror B Concave Mirror C Convex Mirror D Converging Lens E Diverging Lens 16. A Plane Mirror B Concave Mirror C Convex Mirror D Converging Lens E Diverging Lens Hint: For resistors in parallel, the voltage drop is the same across each one. How does power dissipation relate to voltage drop? Solution: The voltage drop across each resistor is the same. dissipation over a resistor is equal to: P = V 2 / R So simply use the given variables in this equation: P = (70 V) 2 / 96 Ω P = W Power The other two resistors do not even come into play in this calculation! 17. A Plane Mirror B Concave Mirror C Convex Mirror D Converging Lens E Diverging Lens 15) 16) 17) onverging Lens oncave Mirror onvex Mirror Consider the RLC circuit shown in the figure. R C V L

6 Select True, False or Cannot tell for the following statements. The current through the inductor always equals the current charging/discharging the capacitor. 18. A True B False C Cannot tell The current through the inductor is the same as the current through the resistor at all times. 19. A True B False C Cannot tell Energy is dissipated in the resistor but not in either the capacitor or the inductor. 20. A True B False C Cannot tell The voltage drop across the resistor is the same as the voltage drop across the inductor at all times. 21. A True B False C Cannot tell A 77 year old man has a near point of 93 cm. What power lens (in diopters) does the man need in order to be able to see an object clearly at the normal near point of 25 cm? Assume that the man will get contact lenses, that is neglect the two centimeters that glasses would be away from the eye. 23. A B 1.39 C ) D 2.92 E 4.24 F 6.15 G 8.92 H [ ] What is the value of the inductance L so that the above circuit carries the largest current? Data: R = Ω, f = Hz, C = F, V rms = V. (in H) 22. A B C D E F G H ) 19) 20) 21) 22) False 1.14E-06 [ e e-06] Unit: H Consider a series RL circuit with R= 70.0 Ω and an unknown inductor L, driven by an AC emf with E rms = 30.0 Volts at frequency f= 7.60 khz. If we measure the current in the circuit, we find I rms = Amps. is the inductance L? (in H) 24. A B C D E F G E H R L What

7 What is the magnitude of the phase angle between the applied voltage and the current? (in deg) 25. A B C D E F G H ) 4.40E-03 [ ] Unit: H 25) 7.16E+01 [ ] Unit: deg A four-turn rectangular coil has a spatially varying magnetic field directed through its center as shown. The magnetic field is given by B = 4.2y 2 t ˆk, where B is in Tesla when t is in s and y is in m. Find the magnitude of the induced emf in the coil. emf = (in V) 26. A B C D E F G H The single slit diffraction pattern shown below was made with light with λ = 630 nm. The screen was 1.6 m from the slit, and the distance to the second minimum (indicated by the arrow) was 5 cm. What is the slit width in mm? Hint: The distance between the center of central maximum and the n th minimum for single slit diffraction is given by x n = (ndλ)/b. n=2 in this case. Solution: Solve for the slit width b and plug in numbers: x n = (ndλ)/b b = (ndλ)/x n In this case, we re given the location of the second minimum, so n=2: And the induced current is 27. A clockwise B counterclockwise 26) 27) H 1.21E-04 [ ] Unit: V clockwise b = (2 1.6 m 630 nm)/5 cm b = (2 1.6 m m)/ m b = mm

8 i 1 q v In the picture below, the two wires carry current i 1 and i 2, respectively, with positive current to the right. The charge q is positive and has velocity v to the right. If v = 0, then the force on q is zero. 28. A True B False i 2 A concave mirror produces a virtual image that is 8 times as tall as the object. If the object is 28 cm in front of the mirror, what is the focal length of this mirror? (in units of cm) 35. A 16.4 B 20.5 C 25.6 D 32.0 E 40.0 F 50.0 G 62.5 H ) 32.0 [ ] Sig 0-15 If i 2 = - i 1 then the force on q equals zero. 29. A True B False If i 2 = 0 and i 1 is greater than zero, then the magnetic field near charge q points out of the page. 30. A True B False If i 2 = 0 and i 1 is greater than zero, then the force on q points into the page. 31. A True B False If i 2 = 0 and i 1 is greater than zero, then the force on q is north. 32. A True B False If i 1 = i 2, then the wires are attracted to each other. 33. A True B False If i 1 is less than i 2, then the force on q is south A True B False 28) 29) 30) 31) 32) 33) 34) False False False

9 You would like to slow down your aging process by traveling very fast relative to Earth on a spaceship. What is the required speed of the spaceship, if you plan to age 17.1 years while everybody else on Earth will age 29.1 years? (in m/s) A soap film made with material of index of refraction n = 1.3 is illuminated by white light. If the reflected light is maximum at λ = 630 nm, what is t, the minimum thickness in nm the film could have had? 36. A B C ) D E F G H E+08 [ ] Unit: m/s Hint: This is a thin film interference problem. The reflected light will be a maximum for t = (m+ )λ/(2n), m = 0,1,2,3,... Solution: So we know we have constuctive intereference when: t = (m + 1 / 2 )λ/(2n), m = 0,1,2,3,... So, what value of m should we use? The question asks what MINIMUM thickness could give rise to this interference. We can see that t will be smallest when m is 0, therefore, we have: An electron has a speed of v = c. What is its total energy (rest energy plus kinetic energy)? (in MeV) 37. A 2.45 B 2.87 C 3.36 D 3.93 E 4.59 F 5.37 G 6.29 H ) 2.87 [ ] Unit: MeV t = 1 / 2 λ/(2n) t = λ/(4n) t = 630 nm / (4 1.3) t = nm Printed from LON-CAPA MSU Licensed under GNU General Public License