PH2200 Practice Final Exam Spring 2004 - Michigan ...gagin/2200f05/textfiles/practicefinal... · Web view19. A beam consisting of red and blue light is incident from air onto a slab

PH2200 Practice Final Exam Spring 2004

Instructions

1. Write your name and student identification number on the answer sheet.

2. This a two-hour exam.

3. Please cover your answer sheet at all times. 4. This is a closed book exam. You may use the PH2200 formula sheet that is included with the exam.*

5. Equations may not be stored in calculators, nor may calculators be exchanged.

6. Record your answers in the form A, B, C, etc, on the answer sheet.

7. This exam consists of 20 concept questions worth six points each and nine problems having a total of 30 parts. The problem parts are equally weighted: each is worth six points. The total number of points on the exam is 300.

8. If you have any questions during the exam, please raise your hand and wait for assistance.

* The formula sheet is omitted from this practice exam.


Concept Questions: Each question has a single correct answer and is worth six points.

1. The figure below shows five pairs of plates: plates A, B and D are charged insulating plates and C is an electrically neutral conducting plate. The electrostatic forces between the plates are shown for three of the pairs. For the remaining two pairs, do the plates repel or attract each other?

A A A B C

B C D D D

(A) B and D repel; C and D repel (B) B and D repel; C and D attract (C) B and D attract: C and D repel (D) B and D attract: C and D attract

2. The figure below shows four situations in which charged particles are fixed in place on an x-axis. In which situation is there a point on the x-axis to the left of the particles where an electron will be in equilibrium? Exclude the point at infinity.

+q -q +q -2q +2q -q +2q +2q

(A) (B) (C) (D)

The following two questions refer to the figure to the right. A spherical shell with a uniform positive surface charge density is near a positive point charge.

3. What type of material is the spherical shell?

(A) Metal (B) Insulator (C) Need more information

4. Is the electric field inside the sphere zero?

(A) Yes (B) No (C) Need more information

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5. One proton is accelerated from rest by a uniform electric field while a second proton is accelerated from rest by a non-uniform electric field. The two protons move through the same electric potential difference. Is the final speed of the proton in the uniform electric field greater than, equal to, or less than the final speed of the proton in the non-uniform electric field?

(A) Greater than (B) Equal to (C) Less than (D) Not enough information is given

The figure to the right applies to the next two questions. A capacitor C is made of two parallel plates separated by a distance d. The dimensions of the plates are very large when compared with d. This capacitor is connected to a battery with emf and a switch as shown. The switch is initially closed.

6. With the switch closed, the electric potential of plate A is higher than the electric potential of plate B.

(A) True (B) False

7. Let E be the magnitude of the electric field between the plates when the switch is closed. At , the switch is opened, and then the plates of the capacitor are pushed closer to a distance . The magnitude of the electric field, , between the plates after making these changes is

(A) (B) (C)

8. Two types of resistors are made of the same material. A type 1 resistor has twice the diameter of a type 2 resistor but is half as long as the type 2 resistor. Which of the configurations shown has the higher net resistance?

(A) A (B) B (C) A and B have the same resistance.

3

A – Type 1 B – Type 2

+-

A

BC

PH2200 Practice Final Exam Spring 2004 9. An ordinary resistive light bulb and a resistor R are in series with a battery that provides an emf . The circuit is first at room temperature, and then the resistor R is immersed in liquid nitrogen so that its temperature is significantly decreased. As a result of this change,

(A) the bulb glows more brightly because R increases. (B) the bulb glows more brightly because R decreases. (C) the bulb glows less brightly because R increases. (D) the bulb glows less brightly because R decreases.

(E) there is no change in the brightness of the bulb.

The figure to the right applies to the next two questions. Three particles having the same charge and the same speed, but differing in mass, enter a region of uniform magnetic field directed into the plane of the page.

10. Which particle has the largest mass?

(A) particle A (B) particle B (C) particle C (D) Not enough information is given

11. A uniform electric field is now applied in the region of the magnetic field so that particles continue to move up toward the top of the page without being deflected. What should be the direction of this electric field?

(A) right (B) left (C) up (D) down (E) into the page

12. A point charge +Q is placed at the end of the second-hand of a watch, as shown in the figure. What is the direction of the magnetic field at the center of the watch due to this moving charge?

(A) into the page (B) out of the page

(C) depends on the position of the charge

4

A B C

A, B, C

1

3

6

9

5


13. Recall that the magnetic field of a long, straight wire consists of circular field lines. Does Ampere's Law hold for a square loop surrounding this wire?

(A) Yes (B) No (C) Not enough information is given

14. There is a wire carrying current out of the paper as shown by a thick circle with a dot in the middle. Concentric circles with arrows outside the wire represent the magnetic field lines. Which one of these diagrams best represents the magnetic field lines?

15. A uniform magnetic field is perpendicular to the paper within the enclosed region indicated by the dots. The four rectangular loops of conducting wire are lying flat on the paper and are moving to the right with the same, constant velocity. The resistance is the same for each loop. At the instant shown in the figure, in which loop is the induced current the largest?

(A) A (B) B (C) C (D) D (E) The induced current is the same in all loops.

16. The energy stored in an inductor depends on the direction of the current passing through it.

(A) True (B) False

6

loop

(A) (B) (C)

(D) (E)

A

BC

D

(C) Not enough information is givenPH2200 Practice Final Exam Spring 2004

17. Two ac generators produce sinusoidal voltages with the same amplitude but different frequencies. How do their rms voltages compare?

(A) The rms voltage of the higher frequency source is greater. (B) The rms voltage of the higher frequency source is less. (C) The rms voltages are equal. (D) Not enough information is given

18. A plane electromagnetic wave (for example, a radio wave) propagates in a vacuum. The electric field of this wave is entirely in the plus and minus z directions in space as described in an xyz coordinate system. Select the incorrect statement about this wave.

(A) The magnetic field of this wave must be entirely in the x-y plane. (B) If the magnetic field of this wave is entirely in the plus and minus x directions, the electromagnetic wave is propagating in either the plus or minus y direction. (C) Assuming that the maximum electric field is unchanged, the energy density associated with the wave increases when the frequency of the wave is increased. (D) The magnitude of the magnetic field of the wave is a maximum when the magnitude of the electric field is a maximum. (E) The ratio of the maximum value of the electric field of this wave to the maximum value of the magnetic field of the wave is a constant, and this constant has the same value for all plane electromagnetic waves in a vacuum.

19. A beam consisting of red and blue light is incident from air onto a slab of glass. The index of refraction of blue light is greater than that for red. When the light emerges at the bottom,

(A) the red and the blue light emerge at the same point. (B) the red light emerges at a larger value of x along the axis than does the blue light. (C) the blue light emerges at a larger value of x along the axis than does the red light.

20. The person in the figure to the right is 2 m tall. A mirror is located 20 m away and is 0.5 m tall. The top of the mirror is at the same height as the top of the person’s head. Assume for simplicity that the person’s eyes are at the height of the top of his head. What part of his body does the person see in the mirror?

(A) top 0.25 m (B) top 0.5 m (C) top 1 m (D) top 1.5 m (E) entire 2 m

7

xglass

20 m

.5 m

2 m


Problems: Each part of each problem is worth six points.

1. Positronium consists of an electron with charge -e bound by the attractive Coulomb force to its antiparticle, the positron with charge +e. As shown in the figure below, assume the distance between the electron and positron is d. Report all answers in terms of e, d, a, and any necessary physical constants.

+e -e A

d a

(a) What is the magnitude of the electric force exerted on the electron by the positron?

(A) (B) (C) (D) (E) Point A in the figure above is a distance a from the electron on the line connecting the electron and positron.

(b) What is the magnitude of the electric field at point A?

(A) (B) (C) (D) (E) (c) If the electric potential at infinity is taken to be zero, what is the electric potential at point A?

(A) (B) (C) (D) (E) (d) What is the potential energy of positronium?

(A) (B) (C) (D) (E) (F)

8

9


2. In addition to a magnetic field, the Earth also has an electric field. During days of fair weather (no thunderclouds), the atmospheric electric field has a magnitude of 135 V/m at the Earth's surface, and it points toward the center of the Earth. Treat the Earth as an isolated, uniformly charged conducting sphere of radius , and take the zero of electric potential to be at infinity.

E = 135 V/m

(a) What is the net charge (sign and magnitude) on the Earth?

(A) -0.0957 C (B) +0.0957 C (C) (D) (E) (F)

(b) What is the magnitude of the flux of the electric field through a sphere concentric with the Earth but having only half its radius?

(A) 0 (B) (C) (D) (E) (c) What is the electric energy density near the surface of the Earth?

(A) (B) (C) (D) (E)

(d) What is the magnitude of the electric potential of the surface of the Earth?

(A) (B) (C) (D)

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(E)


3. The cable connecting the positive terminal of an automobile battery to the starter motor is 0.600 m long and 0.250 cm in radius. The resistance of the cable is .

(a) What is the resistivity of this cable?

(A) (B) (C) (D) (E)

(b) When the motor is stalled, the current in the cable may be as much as 600 A. What is the potential difference between the ends of the cable under this condition?

(A) 0.316 V (B) 0.547 V (C) 4.57 V (D) 11.7 V (E) 12.0 V

(c) At what rate is heat dissipated in the cable under the condition of part (b), that is, what is the power?

(A) 0.316 W (B) 4.82 W (C) 23.6 W (D) 112 W (E) 189 W

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4. To protect service personnel against shock, large capacitors in the power supplies of electronic equipment are usually connected in parallel with "bleeder resistors" whose job is to discharge ("bleed") the capacitors after the equipment is turned off. Suppose a capacitor with an initial charge of is in parallel with a bleeder resistor.

(a) What is the initial electric potential difference across the capacitor?

(A) (B) (C) 4.56 V (D) 123 V (E) 355 V

(b) How much charge is on the capacitor after a time corresponding to one time constant?

(A) (B) (C) (D) (E)

(c) How much time will it take for the capacitor voltage to reach the safe value of 30.0 V?

(A) 8.85 s (B) 11.2 s (C) 19.2 s (D) 27.7 s (E) 35.0 s

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5. At the surface of a pulsar or neutron star the magnetic field may be as strong as 108 T. A proton with a speed of is on the surface of such a pulsar. Consult the figure below for the direction of the magnetic field and the proton’s initial velocity. Assume that in the region of interest the magnetic field is uniform with a magnitude of 1.00 x 108 T.

z

y

x (out of page)

(a) What is the direction of the magnetic force on the proton?

(A) +x (B) -x (C) +y (D) -y (E) +z (F) -z (b) What is the magnitude of the magnetic force on the proton?

(A) (B) (C) (D) (E)

(c) What is the shape of the path or trajectory of the proton?

(A) straight line (B) ellipse (C) circle (D) parabola (E) hyperbola

(d) What is the cyclotron frequency of the proton in the given field?

(A) (B) (C) (D)

13

(E)

14


6. A long cylindrical conductor having a radius of carries a current of 10.0 A uniformly distributed over its cross-section. A long thin wire lies parallel to the cylinder, a distance of 0.500 m from its center, and carries a current of 2.00 A in the same direction as that in the cylinder. In the figure below, both currents are out of the page. 10.0 A (out)

2.00 A (out)

0.500 m

(a) What is the magnitude of the magnetic field produced by the cylindrical conductor a distance of 0.500 m from its center?

(A) (B) (C) (D) (E)

(b) What is the magnitude of the magnetic force per unit length experienced by the long thin wire?

(A) (B) (C) (D) (E)

(c) Suppose the long thin wire is now removed. What is the magnitude of the magnetic field at a point inside the cylindrical conductor, a distance of from its center?

(A) (B) (C) (D) (E)

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7. A car alternator consists of a 250-turn coil 5.00 cm in radius in a magnetic field of 0.100 T. The alternator is turning with a constant angular speed of 105 rad/s. This implies that angle shown in the figure below is given by where t is time expressed in seconds.

(a) Find the induced emf in the coil as a function of time.

(A)

(B)

(C)

(D)

(E)

(b) If the angular speed of the coil were doubled, by what factor would the maximum induced emf increase?

(A) 2 (B) 4 (C) 8 (D) 16 (E) There would be no change.

(c) What is the orientation of the coil with respect to the magnetic field when the maximum induced emf occurs, that is, for what angle is the induced emf maximum?

(A) 0 (B) 22.5 (C) 45.0 (D) 67.6 (E) 90.0

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8. A laser beam of wavelength 632 nm and cross-sectional diameter d = 2.00 mm is incident at an angle of = 40.0 on a glass plate having a thickness of t = 2.00 cm. The index of refraction of the glass is 1.55.

(a) At what angle is the laser beam refracted as it passes from air into the glass?

(A) 17.4 (B) 21.3 (C) 24.5 (D) 35.6 (E) 85.0

(b) What is the wavelength of the laser beam inside the glass?

(A) 408 nm (B) 556 nm (C) 632 nm (D) 825 nm (E) 980 nm

(c) What is the cross-sectional diameter of the laser beam after it has passed through the glass plate?

(A) 1.02 mm (B) 1.24 mm (C) 1.69 mm (D) 1.80 mm (E) 2.00 mm

17

glass

t

d


9. When a woman's hand mirror is held 20.0 cm from her face, a virtual image is formed 30.0 cm from the mirror. The mirror is spherical.

(a) What is the radius of curvature of the mirror?

(A) -12.0 cm (B) +12.0 cm (C) +24.0 cm (D) +60.0 cm (E) +120 cm

(b) What is the magnification provided by the mirror for the given object and image distances?

(A) -3.00 (B) -1.50 (C) +1.00 (D) +1.50 (E) +3.00

(c) If the mirror were flat, how far from the woman's face would the image be formed if the mirror were held 20.0 cm from her face?

(A) 20.0 cm (B) 40.0 cm (C) 80.0 cm (D) 120 cm (E) The image would be formed at the same position as the woman's face.

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Name: ____________________________________ ID# ___________________________________________

Recitation Section: 8:00 Zhou _____ 9:00 Zhou _____ 10:00 Teboh _____ 11:00 Teboh _____

12:00 Yap _____ 1:00 Roy _____ 2:00 Roy _____

Concept Questions Problems

D A C B D E1. _______ 11. _______ 1. (a) _______ 3. (a) _______ 6. (a) _______ 9.(a) _______

B A A A A D2. _______ 12. _______ (b) _______ (b) _______ (b) _______ (b) _______

B A B E B B3. _______ 13. _______ (c) _______ (c) _______ (c) _______ (c) _______

B B D E C4. _______ 14. _______ (d) _______ 4. (a) _______ 7. (a) _______

B C C B A5. _______ 15. _______ 2. (a) _______ (b) _______ (b) _______

A B A D E6. _______ 16. _______ (b) _______ (c) _______ (c) _______

B C B A C7. _______ 17. _______ (c) _______ 5. (a) _______ 8. (a) _______

B C D B A8. _______ 18. _______ (d) _______ (b) _______ (b) _______ B B C E 9. _______ 19. _______ (c) _______ (c) _______ C C A 10. _______ 20. _______ (d) _______

10 10 8 10 9 3 _______ _______ _______ _______ _______ _______

Column Subtotals

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Exam Score ___________

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PH2200 Practice Final Exam Spring 2004 - Michigan ...gagin/2200f05/textfiles/practicefinal... · Web view19. A beam consisting of red and blue light is incident from air onto a slab