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Form # listed as VERSION # on bottom of each page Physics 240 Third Exam Fall 2011 1. Last Name:____________________ First Name:_____________________ 2. Please circle your discussion instructor and section below:

Instructor Time Section

David Gidley 9-10 100

David Winn 10-11 200

David Winn 11-noon 300

3. Special Scantron Instructions:

a) Bubble in UNIQ-NAME in “last name” field b) Bubble in 8 digit UM student ID number—this is critical c) Bubble in Form #=version# (critical) and section number d) Print your name in shaded upper right signature box

4. There are 20 multiple choice problems worth 1 points each for a total of 20 points. Choose the one best answer and transfer it to the scantron sheet. You must mark the correct answer on the scantron sheet to get credit for the problem. There is no penalty for guessing, so be sure to enter an answer for every question even if it is just a best guess. 5. At the end of the exam hand in both your scantron and exam booklet in separate piles set up by the proctors. 6. This is a closed book, 90 minute exam. Turn off and put away all electronic devices. You may use a calculator and three 3”x5” note card or equivalent. k = 1/4πε0 =9x109 Nm2/C2 ε0 = 8.85x10-12 C2/Nm2 e = 1.6x10-19 C 1 eV= 1.6x10-19 J μ = micro =10-6 g = 9.8 m/s2 me = 9.1 x 10-31 kg MP=1.67 x 10-27 kg µ0= 4π x 10-7 Tm/A

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1. A wire is wrapped 250 times around a ferromagnetic nickel cylinder of length 10 cm and radius 2 cm and a relative magnetic permeability of 100. When a current of 45 mA runs through the wire what fraction of the magnetic field inside the nickel comes from atomic currents? A) 9% B) 100% C) 1% D) 45% E) 99%

2. Two very long parallel wires carry currents I and 3I and are located at x = -2 m and x = +2 m respectively. Where along x could we place another parallel wire with current 2I pointing down such that the force on this third wire is zero?

A) x = -3 m B) x = 0 m C) x = +3 m D) x = -1 m E) x = +1 m

X (m) -5 -3 -4 0 -1 1 3 4 5

I 3I

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3. When a permanent iron magnet is heated to a glowing red-hot temperature: A) it loses its magnetism B) nothing happens C) the N and S poles reverse polarity D) it becomes an induced magnet E) its magnetic permeability increases

4. 15 seconds after closing the switch the current flowing through the battery is:

A) 17 A B) 3 A C) 30 A D) 45 A E) 12 A

5. A cylindrical region of radius R contains a uniform electric field, parallel to its axis, with

magnitude that is exponentially decaying with time, 0( )t

E t E e τ−

= . The circulation of the magnetic field, B dl⋅∫

, around a concentric circular path of radius r at a particular moment in time inside the cylinder is proportional to: A) r

Re−

B) r C) r2 D) 1/r E) 1/r2

6 V 2 H

L

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6. In the circuit pictured what is the current through the battery a very long time after the switch is closed?

A)

1

IRε

=

B)

2

IRε

=

C)

1 2

IR Rε

=+

D) 1 2

1 2

R RIR R

ε +=

E) /

IL Cε

=

7. You are stuck on a deserted island and need to radio for help. You have constructed a hand-crank generator that can put out an emf of 20 Volts when you turn the crank at 2 Hz. Your two-way radio has an internal resistance of 10 Ohms, and you estimate that you will need to power it with at least 300 Watts to communicate with the closest civilized island. Which of the following transformer turn ratios will give you closest to the minimum necessary power? A) 3:1 step-up B) 6:1 step-down C) 6:1 step-up D) 1:1 E) 3:1 step-down

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8. An important consideration in the transmission of high frequency signals (such as cable

TV) is the characteristic impedance ( 0LZC

≈ ) of the transmission line (where L and C

are the inductance and capacitance of the transmission line per meter, respectively). RG-6 cable, which is used for cable TV signals, has a characteristic impedance of 75 Ω.

One brand of RG-6 cable has a wire of diameter 1 mm surrounded by a conducting shell of diameter 4.72 mm. The space between the wire and the shell is filled with an insulator with dielectric constant k=1.48 and relative permeability km=1. Calculate L, the inductance per meter of this coaxial cable. (μ=10-6) A) 5.3 μH/m B) 10.1 μH/m C) 15.6 μH/m D) 1.2 μH/m E) 0.31 μH/m

9. A 1 meter long solenoid electromagnet is wound with 2000 turns of wire on a ferromagnetic cylinder with relative permeability Km=2700 and cross sectional area of 0.001 m2. What is the self inductance of this electromagnet? A) 1.5 H B) 0.018 H C) 52 H D) 0.065 H E) 14 H

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10. The four wire loops shown have edge lengths of either L, 2L, or 3L. They will move with the same speed into a region of uniform magnetic field B directed out of the page. Rank them according to the maximum magnitude of the induced emf, from least to greatest.

A) 3 and 4 tie, then 1 and 2 tie B) 1, 3, 2, 4 C) 1 and 2 tie, then 3 and 4 tie D) 4, 2, 3, 1 E) 1, then 2 and 3 tie, then 4

11. An electric field 0 sin(2 )E E ftπ= is applied along the axis of a cylindrical semi-conductor of cross-sectional area A=10 cm2 and resistivity 2000 mρ = Ω . For which of the following frequency ranges are both conduction current and displacement current likely to be important? (kilo=103, Mega=106, Giga=109) A) 5 GHz > f > 50 MHz B) f < 500 kHz C) f > 500 GHz D) 50 MHz > f > 500 kHz E) 500 GHz > f > 5 GHz

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12. The resistance R in the rail gun pictured below is 100 Ohms, length L = 50 cm, the mass of the rod is 2 kg, and the battery voltage is 120 Volts. If a 2 Tesla magnetic field is directed out of the page what is the rate at which energy is dissipated as heat in R when the rod is moving at its terminal velocity?

A) infinite, since there is no upper limit to the rods velocity B) 1440 W C) 42 W D) 144 W E) 0 W

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13. Consider the inductor L in the circuit. If the current in the circuit is 0( ) cos( )I t I tω=

then what is the voltage difference a bV V− across the inductor at time 2

t πω

= ?

A) 0 B) 0I Lω+ C) 0I Lω− D) 0

2I Lω

−

E) 0

2I Lω

+

14. An LC circuit has a natural frequency of f= 1.2 x 106 cycles per second (Hz). The diagram shows the system at t = 0 when there is no charge on the capacitor and the current of 1.5 Amps is in the direction shown. What will be the maximum potential difference across the capacitor at some later time? (m=10-3)

A) 3.16 x 10-1 V B) 5.61 x 102 V C) 9.21 x 101 V D) 2.26 x 103 V E) 2.08 x 10-7 V

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15. A 10 meter by 2 meter sheet of copper that is 2 cm thick carries a current of 100 Amps parallel to its 10 meter side. What is the magnetic field inside the sheet 0.3 cm above the center of the sheet? A) 6.28 x 10-7 T B) 5.28 x 10-6 T C) 3.14 x 10-5 T D) 3.14 x 10-7 T E) 9.42 x 10-6 T

16. A steady current I0 is flowing from left to right in the solenoid. A thin copper plate suspended from a high ceiling is placed at rest near the solenoid. The current in the solenoid is then linearly decreased to zero in 5 seconds and then linearly ramped back up to I0 in the opposite direction (right to left). Which observation is the most accurate?

A) The copper plate is attracted to the solenoid throughout the 10 seconds B) The copper plate is first attracted and then repelled from the solenoid C) The copper plate is repelled from the solenoid throughout the 10 seconds D) The copper plate is first repelled and then attracted to the solenoid E) The copper plate remains stationary

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17. The solid circle of radius R in the diagram shows the cross section of a round conducting wire carrying current into the page. The dashed concentric circles are four integration paths in a plane perpendicular to the wire axis that have radii of r1 = R/4, r2 = R/2, r3 =2R, and r4 = 3R. Rank the paths according to the magnitude of the magnetic field B along each path, least to greatest.

A) all tie B) 4, 3, 2, 1 C) 1, 4, then 2 and 3 tie D) 1, then 2 and 4 tie, then 3 E) 4, 1, 3, 2

3 1 2

R

4

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18. A certain region in space contains no currents. It is found that the magnetic field in the region does not vary in time and points up and increases in magnitude as you move to the right. Which one of the following statements is consistent with Maxwell's equations?

A) There is a uniform constant electric field pointing down in the opposite direction to

B

B) There is a constant electric field E

pointing into the page C) There is an electric field pointing into the page that is increasing with time D) There is a constant electric field E

pointing to the right E) There is an electric field pointing into the page that is decreasing with time

B

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19. You have a solenoid with unknown inductance L and unknown internal resistance ri that is not negligible. You hook the solenoid in series with an ideal battery, a switch, and an external resistor with R = 100 Ω. After closing the switch the voltage across the solenoid terminals is observed to start at 50 V and then drop asymptotically to 15 V, as shown in the diagram. What is the approximate value of L?

A) 0.9 H B) 2.2 H C) 1.4 H D) 0.1 H E) 0.4 H

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20. Current I is charging a circular parallel plate capacitor. The circulation of the magnetic field, B dl⋅∫

, around a coaxial circular path between the plates with radius one-half the radius of the plates has some definite value. Consider two surfaces bounded by this circular path; the round flat surface (shaded); and the open soup-can (dashed). What can we conclude from the Ampere-Maxwell Law?

A)

There must be conduction current 4I flowing radially outward in the capacitor plate

through the soup-can sides B)

There must be conduction current 34I flowing radially outward in the capacitor plate

through the soup-can sides C) all of the electric field lines in the capacitor pass through the shaded flat surface. D) There must be displacement current equal to I flowing to the right through the shaded

surface. E) The current (conduction + displacement) through the soup-can is not equal to the

current (conduction + displacement) through the shaded surface.

I

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Answer Key

1. E 2. D 3. A 4. D 5. C 6. A 7. A 8. E 9. E

10. E 11. D 12. E 13. C 14. D 15. E 16. B 17. C 18. E 19. E 20. B