Download Physics 202 – Final (Monday, December 15) – Fall 2014 (Saslow

Physics 202 – Final (Monday, December 15) – Fall 2014 (Saslow)
Name (printed)
Lab Section(+2 pts)
Name (signed as on ID)
Show all work. Partial credit will be given, if earned. Write your answers in the blanks provided. Include the
correct plus or minus 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.
1. Consider a conductor with a cavity containing an unknown charge. The conductor is in equilibrium. The total
charge on the conductor itself is −5 units. If we associate 3 field lines with each unit of charge, then when viewed
from afar there is a net of 12 field lines pointing into the conductor, which is in equilibrium.
a. (4 pts) How much charge is within the cavity?
b. (2 pts) How much charge is on the inner surface of the conductor?
c. (2 pts) On the outer surface?
d. (2 pts) In the bulk?
2. Consider three capacitors. C1 = 6 µF (micro=µ = 10−6 ) and C2 = 12 µF are in series, and C3 = 10 µF is in
parallel with them. Vc = 6 V and the upper plate of C1 has Q1 = 18µ C.
a. (4 pts) Find Va and Vb .
b. (6 pts) Find the voltage differences ∆V1 , ∆V2 , ∆V3 .
c. (4 pts) Find the charges Q2 , Q3 .
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3. An electron in vacuum starts from rest at A, and accelerates upward in a slightly non-uniform electric field to
B. The potential changes by 6 volts when the electron moves by 4 cm.
~
a. (3 pts) What is the direction of E?
b. (3 pts) Is the potential higher or lower at B?
~
c. (3 pts) Estimate |E|.
d. (6 pts) How fast is the electron moving at B?
4. A voltaic cell has internal resistance r = 0.1 Ω and open circuit voltages across the left and right electrodes of
−0.2 V and 1.7 V. It thus has a net emf of E = 1.5 V. It is in series with a resistor R = 0.4 Ω. Let Vd = 0.5 V.
The connecting wires have zero resistance.
a. (12 pts) Find the current, the voltage drops across the resistances, and the voltages at a, b, and c. Using that
information, on the figure on the right, sketch the voltage on going around the cell.
Answers: I =
, ∆Vr =
, ∆VR =
, Va =
, Vb =
, Vc =
b. (3 pts) If the voltaic cell discharges in 20 minutes, find its initial “charge”.
5. A point charge q is held fixed at the origin. At point P (x = 4 cm, y = 3 cm) it produces a field with
x-component Ex = 1.5 N/C.
~ at point P.
a. (2 pts) Find |E|
b. (4 pts) Find q.
c. (4 pts) Find the voltage q produces at x = 3 cm, y = −4 cm.
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6. Two large parallel metal plates are separated by 8.0 mm. Between the plates are a uniform magnetic field
B = 0.3 T pointing into the page and a uniform electric field E. A particle with charge q = −6.0 × 10−12 C travels,
undeflected, rightward between the plates with speed v = 5.0 × 103 m/s.
a) (4 pts) When the particle is between the plates, find the magnitude and direction of the force on the particle
due to the magnetic field.
b) (4 pts) Find the magnitude and direction of the electric field between the plates.
~ points into the paper. A wire carries current to the left. Give the direction of the
7. (5 pts) A uniform field B
force on the wire.
a.
b.
c.
d.
e.
Right
Left
Up
Down
Other
8. A circular loop of conducting wire in the the plane of the page, carrying current clockwise. A permanent
magnet is above the page, its north pole pointing at you.
a. (3 pts) Indicate the equivalent permanent magnet for the current loop (an electromagnet).
b. (3 pts) Find the direction of the force on the current loop.
9. A conducting rod is given a rightward impulse on a track in a magnetic field that points into (x’s) the plane of
the track. Let the length of the resistor arm be l = 4 cm. Take v = 6 cm/sec, R = 2 ohm, B = 5 × 10−2 T.
a. (3 pts) By Lenz’s law, does the circuit tend to expand or contract?
b. (3 pts) What is the direction of the magnetic force on the rod?
c. (6 pts) What is the magnitude of the magnetic force on the rod?
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10. (10 pts) The wire on the left (right) carries current I into (out of) the page. The wires are separated by S = 6
cm. The field of the one on the right has magnitude 8 mT at point A, where y = 3 cm.
a. (4 pts) 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 6 V has an arm with R1 = 4 ohm in parallel with an arm having R2 = 0.04 ohm and L = 12 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 R1 and R2 just after the switch is disconnected.
c. (4 pts) Find the voltage drops ∆V1,2 across each resistor.
d. (4 pts) Find the voltage drop VL across L.
e. (4 pts) From VL = L∆I/∆t, estimate ∆I/∆t just after disconnection.
12. Loops 1 and 2 have the same radius; loop 1 is on the page and loop 2 rests above loop 1. Loop 1carries
clockwise current; suddenly its current is shut off.
a. (4 pts) Find the direction of the induced emf in loop 2.
b. (3 pts) Does loop 2 tend to be attracted or repelled by loop 1?
c. (3 pts) Does loop 2 tend to expand or contract?
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13. (5 pts) Two identical long magnets are along the same line. Each has qm = 5 × 10−4 A-m, face area
A = 6 × 10−6 m2 , and l = 18 cm. Their nearest poles are both N, and are 2.5 cm apart. Find the force acting on
the right N pole due to the left N pole.
14. (8 pts) Unpolarized light of initial intensity 14.0 W/m2 is passed through three polarizing filters. Viewed in the
direction the light is traveling, the axis of the first polarizing filter is horizontal. the axis of the second polarizing
filter is at 60.0◦ clockwise from the horizontal, and the axis of the third polarizing filter is again horizontal. What
is the intensity of the light after it has passed through all three polarizing filters?
15. (6 pts) Without corrective lenses, Frank can’t focus clearly on objects that are further than 120.0 cm. What
is the focal length of the contact lens that will allow him to see objects clearly that are 12.0 m from his eye?
16. (5 pts) Light is incident on a horizontal screen used for a single-slit diffraction experiment. Sketch intensity
(vertical axis) versus position on the screen.
17. (10 pts) Light traveling in air is incident perpendicular to the surface of a 250 nm thick film of plastic (refractive index 1.55) that is on the surface of a sheet of glass (refractive index 1.40). For what wavelengths of light
(in air) within the limits of the visible spectrum (400 nm to 700 nm) is there destructive interference between the
light reflected from the top and bottom surfaces of the plastic film?
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18. A diverging lens with focal length f1 = −20.0 cm is 10.0 cm to the left of a converging lens that has focal
length f2 = 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 lenses.
a) (4 pts) What is the object distance for the second lens?
(Hint: Use s1 , s01 , s2 , s02 notation.)
b) (4 pts) How far is the final image from the converging lens?
c) (4 pts) ls the final image to the left or to the right of the converging lens?
d) (4 pts) Is the final image upright or inverted?
e) (4 pts) What is the height of the final image?
19. Monochromatic light of wavelength 500 nm passes rightward through two narrow slits 2 µm apart. A screen
is 2.4 m away from the slit.
(a) (4 pts) Find the vertical displacement of the first minimum.
(b) (4 pts) Find the largest angle for which there will be a distinct maximum.
20. (8 pts) For a certain metal surface, the longest wavelength of light that will produce photoelectrons is 300
nm. For what wavelength of light will the photoelectrons from this surface have a maximum kinetic energy of 3.0
eV?
21. (8 pts) A right-ward photon of wavelength 600 nm is completely absorbed by a blackened surface on an object
of mass 3 g. Find how many such photons must be absorbed to give the object a velocity of 2 mm/s.
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Here is some useful information for this page.
(p) mp = 1.00727647 u,
Element
Hydrogen
Deuterium
Helium
Helium
Lithium
Lithium
Symbol
H, 11 H
D, 21 H
He, 32 He
He, 42 He
Li, 63 Li
Li, 73 L
(n) mn = 1.00866492 u,
Atomic number Z
1
1
2
2
3
3
(e) me = 0.00054858 u,
Neutron number N
0
1
1
2
3
4
(anti − neutrino ν̄) mν = 0
Atomic mass in u
1.007825
2.014101
3.016029
4.002503
6.015123
7.016005
Mass number A
1
2
3
4
6
7
Table 1: Atomic masses of light elements.
22. (5 pts) Calculate the total binding energy of the nucleus He(4,2).
23. The neutron decays into a p, an n, and a massless ν̄: n→ p + e + ν̄.
a. (5 pts) Find the mass defect of the neutron (in kg).
b. (3 pts) Find the kinetic energy released (in MeV) when the neutron decays.
24. The nucleus Ca(47,20) is a beta-emitter with a half-life of 4.5 days.
a) (3 pts) How many neutrons are in the daughter nucleus produced by this decay?
b) (4 pts) For a 9.0 g sample of this isotope, find how many beta-particles will be emitted per second.
c) (4 pts) Find many grams of this isotope remain in the sample after a week.
25. The gold nucleus Au(198,79) undergoes alpha decay with a half-life of 2.70 days.
a.) (4 pts) Find how many neutrons and protons are in the daughter nucleus produced by this decay.
b) (4 pts) Find the activity in Bq (decays/sec) of a sample that contains 5.0 grams of Au(198,79) nuclei.
26. (5 pts) A 2.5 kg suitcase at an airport absorbs 2.0 × 10−3 J/kg from 100 keV x-rays. How many photons are
absorbed?
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