Physics 212
Homework for Unit 27: Electricity & Magnetism
Spring 2014
To get credit for the homework problems, you must include all of the following: All problems should include a
reference to the Activity Guide activity or activities that are related to the problem, a discussion of how the
activity is related, and a discussion of the concepts that were learned in the activity. Answer the following for
each question (What activity or activities from the Activity Guide are related to this problem, how is the activity
related, and what concepts were learned in the activity?
Problem 1
Two parallel conductors are each 0.5 m long and carry 10 mA currents in opposite directions.
a. What center-to-center separation must the conductors have if they are to repel each
other with a force of 1.0 N?
b. Is this physically possible?
Problem 2
The diagram the follows shows the cross section of a wire that is perpendicular to the plane of
the paper. Suppose a compass in placed at location A which is a distance r from the wire and
that points in the direction shown in the diagram.
a. Resketch the diagram and draw arrows to show what direction you expect the compass
to point if it were moved to locations B and C. Note: Use the symbol • in the middle of
the wire if the flow is out of the page and the symbol × in the middle of the wire if the
flow is into the page.
b. Indicate what direction positive current is flowing through the wire and describe the rule
you are using to deduce the direction of current in the wire.
c. What is the direction of the flow of elections through the wire?
Problem 3
A uniform magnetic field is directed toward the right in the plane of the paper as shown in the
diagram that follows. A wire lying perpendicular to the plane of the paper at location A carries
a current I. Suppose that the resultant magnetic field at point D due to a superposition of the
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Physics 212
Homework for Unit 27: Electricity & Magnetism
Spring 2014
uniform magnetic field of magnitude B and the magnetic field of the wire of magnitude Bw is
zero.
a. Is the direction of the current in the wire into or out of the paper? Explain how you
arrived at your conclusion.
b. Assume point A lies at the same distance from the center of the wire as point D and that
the length of the vector assigned to represent the magnitude of the uniform external
magnetic field is that shown on the right. Construct a vector diagram showing the
resultant magnetic field vector Br at point A.
c. Assume that point C is twice the distance from the center of the wire as point D.
Construct a vector diagram showing the resultant magnetic field vector, Br, at point C.
Problem 4
Four long parallel wires each carry a current of 1.0 A. The current direction is
out of the page through wires 1 and 3 and into the page through wires 2 and 4.
Use Ampere's Law to calculate the magnitude and direction of the magnetic
field at point C located at the center of the square. The diagram to the right
represents a scale drawing of the actual "square" and you can use
measurements to obtain any distances you need to complete this problem.
× 2
1
A
3
Problem 5
The earth's magnetic field at either pole is about 0.7 G = 7 × 10-5 T. Using a model in which you
assume that this field is produced by a current loop around the equator, determine the current
that would generate such a field. (Re = 6.37 × 106 m.)
Problem 6
A plane loop of wire consisting of a single turn of cross-sectional area 8.0 cm2 is perpendicular
to a magnetic field that increases uniformly in magnitude from 0.5 T to 2.5 T in a time of 1.0 s.
What is the resulting induced current if the coil has a total resistance of 2 Ω?
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× 4
Physics 212
Homework for Unit 27: Electricity & Magnetism
Spring 2014
Problem 7
The plane of a rectangular coil of dimensions 5 cm by 8 cm is perpendicular to the direction of a
magnetic field B. If the coil has 75 turns and a total resistance of 8 Ω, at what rate must the
magnitude of B change in order to induce a current of 0.1 A in the windings of the coil?
Problem 8
In the arrangement shown in figure below, a conducting bar moves to the right along parallel,
frictionless conducting rails connected on one end by a 6 Ω resistor. A 2.5-T magnetic field is
directed into the paper. Let L = 1.2 m and neglect the mass of the bar.
a. Calculate the applied force required to move the bar to the right at a constant speed of
2 m/s.
b. At what rate is energy dissipated in the resistor?
Problem 9
An engineer has designed a set up with a small pickup coil placed in the center of a large field
coil as shown in the figure that follows. Both coils have many turns of conducting wire. The
field coil produces a magnetic field that is proportional in magnitude to the amount of current
flowing through its wires. The pickup coil is smaller and its many turns can sense or “pickup”
changing magnetic field in the field coil by producing an EMF which is proportional in
magnitude to the rate of change of the magnetic field and the angle between the normal to
field coil and the normal to the pickup coil.
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Physics 212
Homework for Unit 27: Electricity & Magnetism
Spring 2014
You have been hired as a consultant to check on the reliability of the Engineer’s work and you
figure out how to use Faraday’s Law along with proportional reasoning to check on the validity
of the results that have been reported without doing any formal calculations or measurements.
If the Engineer has done good work, what does she have sketched in her laboratory notebook
for each of the situations shown at the very end of this set of problems?
a. Look at graph pair A. Sketch the measured EMF induced in the pickup coil if the
Engineer has adjusted the scope so the maximum EMF is right on the first positive grid
line and the minimum EMF is right on the first negative grid line. Assume the normal to
each of the coils is pointing in the same direction.
b. According to the Engineer’s notebook she has fed exactly the same pattern of current to
the field coil as before but she turned the pickup coil so its normal makes an angle of
+45o with respect to the normal to the plane of the field coil. Carefully sketch the
pattern of EMF observed in the field coil. What is the maximum and minimum
amplitude of the EMF in “grid” units?
c. What happens when she flips the pickup coil over around so it’s normal is 180o from the
normal to the field coil? Sketch the EMF and use the correct signs for the values of the
induced EMF for this situation case. Explain the reasons for the shape and magnitude
of your sketch in each case.
Field Coil
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A.
Em
I
-
Pickup Coil
+
Field Coil
–
Emf
+
–
Physics 212
Homework for Unit 27: Electricity & Magnetism
Spring 2014
Problem 10
You are still double-checking the work of the Engineer. Consider graph B.
Pickup Coil
Field Coil
Fi e l d Co i l
Emf
I
-
+
B.
–
Emf
+
Field Coil
–
a. What should our honest and competent engineer have reported for the pattern of EMF
values as a function of time? Assume that once again the normal to the pickup coil is in
the same direction as the normal to the field coil. Please take care to sketch not only
the shape of the EMF graph but its proper magnitude using the same gain setting on the
oscilloscope as you did in problem 27-9. Use a solid line for your sketch.
b. Suppose the engineer reduced the number of turns in the pickup coil by a factor of 2
and redid the measurements. Sketch a new graph showing the shape and proper
magnitudes for EMF expected pickup coil EMF using a dotted line. Explain the reasons
for the shape and magnitude of your sketch in each case.
Problem 11
You are still double-checking the work of the Engineer. Assume that the number of turns in
both the field and pickup coils are the same as in problem 27-9 as is the oscilloscope setting.
Consider graph C.
Field Coil
+
Em
I
-
Pickup Coil
Field Coil
–
C.
Emf
+
–
a. What should our honest and competent engineer have reported for the pattern of
current fed into the field coil as a function of time? Assume that once again the normal
to the pickup coil is in the same direction as the normal to the field coil. Please take
care to sketch not only the shape of the field current graph but its proper magnitude
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Physics 212
Homework for Unit 27: Electricity & Magnetism
Spring 2014
using the same gain setting on the oscilloscope as you did in problem 27-9. Use a solid
line for your sketch.
b. Suppose the engineer reduced the number of turns in the pickup coil by a factor of 2 but
adjusted the field current so that the EMF was the same as in part (a), and redid the
measurements. Sketch a new graph showing the shape and proper magnitudes for
current in the field coil using a dotted line. Explain the reasons for the shape and
magnitude of your sketch in each case.
Problem 12
You are still double checking the work of the Engineer. Assume that the number of turns in both
the field and pickup coils are the same as in problem 27-9. Consider graph D. What should our
honest and competent engineer have reported for the pattern of EMF induced in the pickup
coil if the oscilloscope gain is adjusted to give a maximum value of EMF of +2 oscilloscope grid
units and a minimum value of -2 oscilloscope units? Hint: What is the derivative of sine
function? Explain the reasons for the shape and magnitude of your sketch in each case.
Pickup Coil
Field Coil
I
-
6|Page
Field Coil
D.
+
Emf
+
–
–