PH113
Physics III
Test I
Spring 1998/99
Name _________________________
(Please print in UPPER CASE BLOCK
letters)
No books or written notes are allowed. You may use the formula sheet provided, your laptop and
any resources residing on your hard drive. This includes Maple and Working Model. No
network connections are allowed. Any student with a physical connection between the computer
and the network outlet during the test will receive a zero on the test.
Show all your work. No credit will be given for answers appearing without supporting
calculations. Partial credit may be awarded based on clarity and completeness of solution. Maple
calculations (but not Working Model) will be accepted as part of the test paper but must be
handed in on the 3 ½ inch diskette provided by the instructor. All Maple code must be
commented for clarity the same as hand calculations.
1.Two long straight wires parallel to the z-axis of a Cartesian coordinate system are located at
(0, 1.0 cm) and (2.0 cm,0) as shown in the figure below. They carry 2.0 A into the page and
3.0 A out of the page respectively.
(a) On the figure above, draw several B field lines representing the B-field created by each wire
separately. (Be sure to indicate the direction of the B-field on your lines of B.)
(b) Calculate the magnitude and direction of the total B-field at the origin created by both wires
together. (Express the direction as an angle in degrees measured anticlockwise from the positive
x-axis.)
PH113
Physics III
Test I
Spring 1998/99
Page 2 of 4
Initials _______________
(Please use BLOCK letters)
2. Two vertical copper rods are free to slide along fixed horizontal rails as shown in the figure
below. All motion takes place in a uniform magnetic field of 2.50 T. The field is perpendicular to
the plane of the rectangular circuit formed by the rods and the rails. For each of the cases below,
indicate whether the current induced in the rectangular circuit is clockwise, anticlockwise, or
zero.
(a) v1=0, v2 = +3 m/s
The induced current is
(b) v1 = v2 = +3 m/s
The induced current is
(c) v1=+3 m/s, v2 = !3 m/s
The induced current is
(d) v1=!3 m/s, v2 = +3 m/s
The induced current is
(e) Calculate the magnitude of the induced current for case (d).
PH113
Physics III
Test I
Spring 1998/99
Page 3 of 4
Initials _______________
(Please use BLOCK letters)
3. A wire is bent into a right triangle with legs 3.0 cm and 4.0 cm long and placed in a uniform
magnetic field of magnitude 0.50 T. A constant current of 3.0 A is caused to flow
counterclockwise in the wire. Initially, the wire is placed so that its plane is parallel to the B-field
as in “Position I” in the figure below. Later, it is rotated into “Position II” where the plane of the
triangle is perpendicular to the field. In the questions below, assume the wire is stationary in
either position I or position II. Note that the observer’s point of view has been changed for the
two figures.
(a) Draw arrows indicating the direction of the force vector on each of the three wire segments in
both Position I and Position II. (If there is no force on the wire segment, label the segment “no
force”.)
(b) For parts (b) and (c), assume the current flowing in the loop is zero. Calculate the magnetic
flux MB through the triangular loop for
(i) Position I
(ii) Position II
(c) Calculate the magnitude of the magnetic circulation integral
(i) Position I
(ii) Position II
n
B@dl
for
PH113 Physics III
Test I, Spring 1998/99
Page 4 of 4
Name _______________
(Please use BLOCK letters)
4. As part of her Ph. D. work in physics a graduate student must design a sensor to detect failure
of an electromagnet. She chooses to use a square current loop, 3.00 cm on a side oriented
perpendicular to the loop. The magnetic field is highly irregular in the region of the loop. To
estimate the flux through the loop, she mentally divides the area of the loop into nine regular
subsections as indicated by the dashed lines in the figure below. Using a gauss meter (magnetic
field measuring device), she measures the field at the center of each of the subsections. Her
recorded values in tesla are shown in the figure below.
3.0 cm
0.1
0.2
0.3
0.2
0.4 0.6
0.4
0.8
Measured B values
into the page
in units of tesla
1.2
(a) Using the graduate student’s data, calculate the flux through the loop.
(b) If the magnet fails, this flux will drop to zero in 5.0 ms at a uniform rate as shown in the top
graph below. What EMF will be induced in one loop of the rectangular circuit?
(c) The alarm that the sensor will interface to requires at least 0.50 V to trigger reliably. How
many turns should she use in a redesigned coil of the same dimensions?
(d) If the multiple turn loop has a total resistance of 0.030 S, what current is induced in the loop?
In what direction is that current?
(e) The top graph below shows the time dependence of the flux through the loop for a magnet
that fails at t = 0. On the empty graph, sketch the time dependence of the current induced in the
sensor coil.