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Key # listed as VERSION # on bottom of each page

Physics 240 Third Exam Fall 2012

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 your scantron to one of the proctors. You may keep

this exam booklet for your records.

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 Nm

2/C

2 ε0 = 8.85x10

-12 C

2/Nm

2

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. The ferromagnetic core of a transformer is made of laminated iron sheets to:

A) facilitate easy assembly

B) reduce i2R losses in the coils

C) increase the magnetic flux

D) save weight

E) prevent eddy currents

2. An AC generator operating at a frequency of f = 60 cycles/second has an RMS emf of 80

V. It is connected to the leads of a 2.0 x 10-4

F capacitor with negligible resistance.

What is the RMS current supplied by the generator (in A)?

A) 27

B) 13

C) 19

D) 6.0

E) 42

3. The inductor is a solenoid with an internal resistance of R = 0.15 What is the current

flowing through the battery 8 seconds after closing the switch?

A) 30 A

B) 3 A

C) 40 A

D) 18 A

E) 12 A

6 V 2 H

L

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4. A circular coil of wire has 25 turns and has a radius of 0.075 m. The coil is located in a

variable magnetic field whose behavior is shown on the graph. At all times, the

magnetic field is directed at an angle of 75° relative to the normal to the plane of a loop.

What is the average emf induced in the coil in the time interval from t = 5.00 s to 7.50 s?

A) 180 mV

B) 140 mV

C) 18 mV

D) 92 mV

E) 49 mV

5. A cylindrical region of radius R contains a uniform conduction current density, parallel to

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

J t J e

. The

magnitude of the magnetic field at radius r at a particular moment in time inside the

cylindrical region (r<R) is proportional to:

A) r0 (constant)

B) r

C) r2

D) 1/r

E) 1/r2

6. A toroidal solenoid with 400 turns of wire and a mean radius of 6.0 cm carries a current of

0.25 Amps. The wires are wrapped around a core with a relative permeability of 60.

What percentage of the magnetic field within the core of the toroid is produced by atomic

currents?

A) 37%

B) 98%

C) 63%

D) 1.3%

E) 0%

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7. Two of Maxwell's equations contain a path integral on the left side and an area integral

on the right. These equations require that:

A) the area must be well-separated from the path

B) the path must be along a field line and the area must be perpendicular to the field line

C) the area must be flat and contain the path

D) the path must pierce through the area

E) the path must be the boundary of the area

8. Find the magnitude and direction of the magnetic field produced at point P by the current

element shown in the diagram. The lengths in the diagram are x1=40 cm and z1=30 cm.

The current is 5 amps and the current element is 1 cm long. (Note that in the coordinate

system pictured in the diagram the y axis points into the page).

A) 5.3 x 10

-5 T in negative z direction

B) 3.4 x 10-7

T in negative y direction

C) 9.1 x 10-8

T in negative x direction

D) 0 Tesla

E) 1.2 x 10-8

T in negative y direction

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9. The resistance R in the rail gun pictured below is initially 100 Ohms. Consider what

happens to the terminal velocity vt and the initial acceleration a0 at time t=0 if we replace

this resistor with one that is 200 Ohms. (t=0 is the moment you release the rod from rest).

(Note, the bar is sliding on frictionless rails).

A) vt is half and a0 half

B) vt is twice and a0 twice

C) vt is half and a0 is the same

D) vt is the same and a0 half

E) vt is the same and a0 is the same

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10. The solid circle of radius R in the diagram shows the cross section of a long solenoid with

its axis pointing straight into the page. The current in the solenoid is increasing steadily.

The dashed concentric circles are four integration paths in a plane perpendicular to the

solenoid 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 circulation of the electric field, E dl along each

path, least to greatest.

A) 1, then 2 and 4 tie, then 3

B) all tie

C) 4, 1, 3, 2

D) 1, 4, then 2 and 3 tie

E) 1,2, then 3 and 4 tie

3 1 2

R

4

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11. A solid conductor of radius a is supported by insulating disks on the axis of a conducting

tube with inner radius b and outer radius c as shown in the figure. The central conductor

and the tube carry equal currents in opposite directions. The currents are distributed

uniformly over the cross sections of each conductor. Which one of the following

statements about the magnetic field created by this arrangement is FALSE.

A) B is a maximum at r=a.

B) B=0 for r>c

C) B decreases to zero as you go from r=b to r=c.

D) B is proportional to 1/r for r<a

E) B is proportional to 1/r for a<r<b

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12. The AC generator in a hydroelectric power plant supplies a small town with an RMS

current of 4000 A at 120 V rms. At the power plant a 50-to-1 step up transformer is used

prior to high voltage transmission. Near the town a substation has a 100-to-1 step down

transformer and then each house has a nearby 20-to-1 step down transformer to provide a

safe, low voltage. Assuming ideal transformers and no transmission losses what RMS

current must be produced in the AC generator?

A) 141 A

B) 40,000 A

C) 100 A

D) 25 A

E) 1000 A

13. An electric field 0 cos(2 )E E ft is applied along the axis of a cylindrical

semiconductor of cross-sectional area A=20 cm2

and resistivitym At what

frequency, f, are the amplitudes of the conduction and displacement currents equal? (1

Hz = 1 cycle/s)

A) 5.0 x 109 Hz

B) 4.0 x 103 Hz

C) 2.0 x 1011

Hz

D) 8.0 x 105 Hz

E) 9.0 x 108 Hz

HV transmission

20-1

Step down 4000 A rms

50-1

Step up

100-1

Step down

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14. Two concentric circular loops of wire lie in a plane. The inner loop radius, r = 0.1 m, is

much smaller than the outer loop radius of R = 2 m. What is the approximate mutual

inductance of this configuration of two loops?

A) 5.2 x 10

-8 H

B) 8.4 x 10-7

H

C) cannot determine without knowing the current in the outer loop

D) 9.9 x 10-9

H

E) cannot determine without knowing the rate change of current in the outer loop

15. The switch in the circuit below has been closed for a long time. Immediately after

opening the switch what is the rate (in Joules/s = Watts) at which magnetic energy stored

in the inductor, L, is decreasing?

A) 29 W

B) 0 W

C) 48 W

D) 7 W

E) 15 W

r R

L 12 V

20 Ω

60 Ω 2 mH

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16. Current I is charging a circular parallel plate capacitor with plate radius of R. The

circulation of the magnetic field, B dl , around a coaxial circular path between the

plates with r = R/3 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) The "current" (conduction + displacement) through the soup-can is not equal to the

"current" (conduction + displacement) through the shaded surface.

B) The conduction current through the soup-can is equal to the conduction current

through the shaded surface.

C) There must be conduction current (8/9)I flowing radially outward in the capacitor

plate through the soup-can sides

D) There must be conduction current of (3/4)I flowing radially outward in the capacitor

plate through the soup-can sides

E) There must be conduction current equal to (1/9)I flowing to the right through the

shaded surface.

17. In a simple, purely inductive AC circuit a sinusoidally oscillating emf of angular

frequency ω forces AC current to flow through a solenoid of inductance L. This AC

current generates an oscillating magnetic field along the axis of the solenoid. The induced

electric field that circulates around the axis inside the volume of the solenoid is:

A) sinusoidal in time and its amplitude does not depend on ω

B) sinusoidal in time and its amplitude is inversely proportional to ω

C) constant

D) 0, since the inductor/solenoid voltage is 90° out of phase with the current

E) sinusoidal in time and its amplitude is proportional to ω

I

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18. In the circuit below the three resistors are the same at 10 Ω each and the inductor has L =

35 mH. What is the potential difference across the inductor immediately after closing

the switch? We do know that the current through the battery is 4.0 A after the switch has

been closed for a very long time.

A) 10

B) 50 V

C) 15 V

D) 30 V

E) 0

19. Eighteen very long, straight conductors with square cross sections carrying current of 5 A

straight out of the page are laid side by side to form a current sheet as shown in the

diagram. What is the magnitude and direction of the magnetic field at point P, 0.03 m

from one edge of the sheet as shown?

A) 2.8 x 10

-4 T, down

B) 1.5 x 10-5

T, up

C) 6.9 x 10-5

T, up

D) 9.5 x 10-7

T, left

E) 3.2 x 10-6

T, down

L

P 0.03 m

0.12 m

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20. An LC circuit is composed of an ideal solenoid and a capacitor (no resistance in the

circuit). It oscillates at some natural frequency f0. If we now fill the volume of the

solenoid with a ferromagnetic material that has permeability Km = 3000 what happens to

the natural frequency?

A) it is 55 times higher

B) it is 3000 times higher

C) it is unchanged

D) it is 3000 times lower

E) it is 55 times lower

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Answer Key

1. E

2. D

3. D

4. C

5. B

6. B

7. E

8. E

9. D

10. E

11. D

12. C

13. E

14. D

15. A

16. C

17. A

18. D

19. A

20. E