Physics 202 Final (Monday, December 12) Fall 2016 (Saslow) White Version Name (printed) Lab Section(+2 pts) Name (signed as on ID) Show all work. Partial credit may be given. Answers should include the correct sign and the correct units. Total points will be scaled to 100. If your grade on the final exceeds that on your lowest exam, that exam grade will be replaced by the average of that exam and the final. Look at front board for any corrections. 1. Conducting globes A and B, on insulating bases, initially are neutral. An insulating charged rod with Q rod = 5 nc is brought near A, without contact or sparking. Next, holding B by its base, B is contacted to A and then is withdrawn. Finally, the charged rod is removed. Take Q A = 6 nc and Q B = +4 nc. Circle true (T) or false (F) to tell whether the values of Q A and Q B are consistent with the following valid physical statements. a. (3 pts) Opposites attract and likes repel. T or F. b. (3 pts) Charge is conserved. T or F. c. (3 pts) The amount of electrostatic induced charge cannot exceed the amount that produced it. T or F. 2. Consider three capacitors. C 1 = 6 µf (micro=µ = 10 6 ) and C 2 = 3 µf are in series, and C 3 = 10 µf is in parallel with them. V a = 6 V and the upper plate of C 3 has Q 3 = 20 µc. a. (2 pts) Find V 3. b. (4 pts) Find Q 1 and Q 2. c. (4 pts) Find V 1 and V 2. d. (4 pts) Find V b and V c. 1
3. An electron in vacuum starts from rest at A, and accelerates downward in a slightly non-uniform electric field to B. The potential changes by 12 volts when the electron moves by 4 cm. a. (2 pts) Find the direction of E. b. (2 pts) Is the potential higher or lower at B? c. (3 pts) Estimate E. d. (5 pts) Find how fast the electron is moving at B. 4. A voltaic cell has internal resistance r = 0.2 Ω and open circuit voltages across the left and right electrodes of 0.3 V and 0.9 V, for a net emf of E = 1.2 V. It is in series with a resistor R = 0.4 Ω. Let V a = 0.4 V. The connecting wires have zero resistance. a. (12 pts) Find the current, the voltage drops across the resistances, and the voltages at b, c, and d. Using that information, on the figure on the right, sketch the voltage on going around the cell. Answers: I =, V r =, V R =, V b =, V c =, V d = b. (4 pts) If the voltaic cell discharges in 30 minutes, find its initial charge and its initial energy. 5. A point charge q is held fixed at the origin. At point P (x = 6 cm, y = 8 cm) it produces a field with x-component E x = 3.0 N/C. a. (2 pts) Find E at point P. b. (4 pts) Find q. c. (4 pts) If V = 0 at infinity, find the voltage q produces at P. 2
6. Two large vertical parallel metal plates are separated by 12.0 mm. Between them are a uniform magnetic field B of 0.04 T normal to the page (in or out) and a uniform rightward electric field E. A particle with charge q = 4.0 10 12 C travels, undeflected, vertically upward between the plates with speed v = 8.0 10 3 m/s. a) (4 pts) When the particle is between the plates, find the magnitude and direction of the force on the particle due only to the electric field. b) (4 pts) Find the magnitude and direction of the magnetic field between the plates. 7. A uniform field B points into the paper. A wire carries current to the left. a) (3 pts) Give the direction of the force on the wire. b) (3 pts) If the field has magnitude 0.04 T and the current is 2 A, find the force per unit length acting on the wire. 8. A circular loop with current I is along the axis of a permanent magnet. a. (3 pts) Sketch the equivalent electromagnet for the current loop. b. (3 pts) Indicate the direction of the force on the current loop. 9. A current loop of area 4 cm 2 and R = 0.5 ohms is within, and co-axial with, a long solenoid of area 16 cm 2 that has 40 turns/cm. The solenoid carries 2 A counterclockwise. a. (3 pts) If the solenoid current suddenly increases to 3 A, indicate the direction of the current induced in the loop. b. (3 pts) Indicate the direction of the force on the most rightward part of the loop. c. (3 pts) If the solenoid current suddenly decreases to 1 A, indicate the direction of the current induced in the loop. d. (3 pts) Indicate the direction of the force on the most rightward part of the loop. e. (3 pts) If the increase takes place in 2 msec, find the magnitude of the emf acting on the loop. 3
10. (10 pts) The wires on the left (#1) and right (#2), separated by s = 6 cm, carry current I out of the page. The field of the one on the right has magnitude 6 mt at point A, where y = 2.5 cm. a. (4 pts) Find the direction of the net magnetic field at A. b. (6 pts) Find the magnitude of the net magnetic field at A. 11. An emf of 12 V has an arm with R 1 = 6 ohm in parallel with an arm having R 2 = 0.03 ohm and L = 25 mh. The switch is initially closed. At time zero it is disconnected. a. (4 pts) Find the currents (including direction) while the switch is closed. b. (4 pts) Find the currents (including direction) through R 1 and R 2 just after the switch is disconnected. c. (4 pts) Find the voltage drops V 1,2 across each resistor. d. (4 pts) Find the voltage drop V L across L. e. (4 pts) From V L = L I/ t, estimate I/ t just after disconnection. 12. A current of 5 A enters a from the left. r 1 = 3 ohm, r 2 = 6 ohm, r 3 = 4 ohm. Take V b = 2 V. a. (4 pts) Find I 1, I 2, and I 3. b. (4 pts) Find V 1, V 2, and V 3. c. (2 pts) Find V c. 4
13. A 20 cm long magnet is in a non-uniform field, its magnetic moment pointing to the right. It is in a very non-uniform magnetic field, with only its S pole feeling a force, which is 0.002 N to the right. a) (3 pts) If the field at the S pole is 0.05 T, find the pole strength of the S pole. b) (3 pts) For a pole strength of 0.0004 A-m, find the field (including direction) that the N-pole produces at the S-pole. 14. (6 pts) Unpolarized light of initial intensity 14.0 W/m 2 is passed through three polarizing filters. Viewed in the direction the light is traveling, the first filter s axis is vertical. The second filter s axis is 70.0 clockwise from the vertical, and the third filter s axis is 80.0 counterclockwise from the vertical. Find the intensity and polarization of the light after it has passed through all three filters. 15. (4 pts) Without corrective lenses, Frank can t focus clearly on objects that are closer than 80 cm. Find the focal length of the contact lens that will allow him to see objects clearly that are 20 cm from his eye. 16. (4 pts) Light is incident on a horizontal screen used for a two-slit interference experiment. Sketch intensity (horizontal axis) versus position on the screen. 17. (6 pts) Light in air is incident normal to the surface of a 500 nm thick film of plastic (refractive index 1.35) above a sheet of glass (refractive index 1.50). Find the visible wavelengths of light in air (400 nm to 700 nm) is there destructive interference between the light reflected from the top and bottom surfaces of the plastic film. 5
18. A diverging lens with focal length f 1 = 20.0 cm is 10.0 cm to the left of a mirror of focal length f 2 = 60.0 cm. An object that is 2.0 mm tall is placed 12.0 cm to the left of the diverging lens. The final image is formed after the light has passed through both optical devices. a) (3 pts) Find the object distance for the mirror. (Hint: Use s 1, s 1, s 2, s 2 notation.) b) (3 pts) Find how far the final image is from the mirror. c) (3 pts) ls the final image to the left or to the right of the mirror? d) (3 pts) Is the final image upright or inverted? e) (3 pts) Find the height of the final image. 19. Monochromatic light of wavelength 600 nm passes rightward through two narrow slits 2 µm apart. A screen is 2.4 m away from the slit. (a) (3 pts) Find the vertical displacement of the first minimum. (b) (3 pts) Find the largest angle for which there will be a distinct maximum. 20. (4 pts) For a certain metal surface, the longest wavelength of light that will produce photoelectrons is 300 nm. Find the wavelength of light for which photoelectrons emitted from this surface have a maximum kinetic energy of 3.0 ev. 6
21. A right-ward photon of wavelength 600 nm is completely absorbed by a roasted ant of mass 0.3 g. a. (4 pts) Find how many such photons must be absorbed to give the ant a velocity of 2 mm/s. b. (3 pts) Find the center of mass kinetic energy K of the ant due to this absorbed momentum. c. (3 pts) Find the total energy E absorbed by the ant due to the photons. (E K goes into heat.) For the following problems this information may be useful (isotopic masses are given for neutral atoms): m p = 1.00727647 u, m n = 1.00866492 u, m e = 0.00054858 u, m ν = 0, m4 2 He = 4.002503 u. 22. Bi(214,83) decays with a net half-life of 19.9 min. 99.98% of the decays are to Po(214,84) and 0.02% are to Tl(210,81). The Bi has mass 213.998712 u, the Po has mass 213.995201 u, and the Tl has mass 209.900074. a. (4 pts) What kind of decay occurs to Po(214,84), and what is the energy release per decay? b. (4 pts) Find the rate of energy produced by a 0.428 g sample of Bi(214,83). Take the 19.9 min half-life. c. (3 pts) With this sample in the stomach of a simulated 4 kg cat, find the rads (0.01 J/kg-s) produced. Use the cat s mass. d. (2 pts) For this type of radiation, find the rems produced. e. (3 pts) Estimate the half-life if decay were only to Tl(210,81). Hint: Should this partial half-life be longer or shorter than 19.9 min? 23. Tritium H(3,1), of mass 3.0160492 u, beta decays with a 12.32 year half-life to He(3,2), of mass 3.016029 u. a) (4 pts) Find the activity in Bq (decays/sec) of a sample containing 99.0 grams of H(3,1) nuclei. b) (4 pts) Estimate how many grams of H(3,1) remain in the sample after 24.6 years. c) (4 pts) Find the energy release in each decay. 7