PH113
Physics III
Test I
Spring 1996/97
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. The figure below shows four wires lying in the xy-plane. In this region of space there exists a
uniform magnetic field of magnitude 0.600 T directed parallel to the x-axis. Each of the wire
segments is 10.0 cm long and carries a current of 3.00 A in the direction indicated by arrows.
y
d
a
B
30E
45E
b
x
c
z
(a) List the wires by letter (a,b,c,d) in order according to the magnitude of the magnetic force on
each, largest force to smallest.
______
largest
_______
______
______
smallest
(b) On the figure, draw arrows to indicate the direction of the force on each wire.
(c) Calculate the magnitude of the force on wire d.
PH113
Physics III
Test I
Spring 1996/97
Page 2 of 4
Initials _______________
(Please use BLOCK letters)
2. A long straight wire passes through the origin of a Cartesian coordinate system and carries a
current of 6.00 A out of the page parallel to the z-axis.
y
(3,4)
x
I
P (3,0)
(a) On the diagram above, draw several B-field lines indicating the direction and relative strength
of the B-field in the neighborhood of the wire that passes through the origin.
(b) Now assume there is a second wire, parallel to the first but passing through the point with xycoordinates (3.00 cm, 4.00 cm) and carrying a current of 8.00 A out of the page. Find the
magnitude and direction of the total magnetic field at point P located at (3.00 cm, 0).
PH113
Physics III
Test I
Spring 1996/97
Page 3 of 4
Initials _______________
(Please use BLOCK letters)
3. (a) Below are five figures showing wire circuits located in uniform fields, which may be into or
out of the page as indicated. In each case there is a change that may, or may not, induce a current
in the loop. If a current is induced, indicate on the figure the direction of the current on the wire
loop at the exact moment shown. If no current is induced, write “no induced current.” [Note D1
and D2 are two views of the same circuit.]
B
A
C
v
v
h
x
Bar move left
B-field increases with time
Conducting ring shrinks
Coil rotates
v
E
v
D2
D1
v
B-field constant
Top view
(b) Suppose that in figure A the B-field is 0.750 T, the resistor is 0.20 S, the height h of the
circuit is 25.0 cm, at the instant shown x = 20.0 cm, and the bar is traveling to the left at a
constant speed of 5.00 cm/s. Calculate the magnitude of the induced current.
PH113 Physics III
Test I, Spring 1996/97
Page 4 of 4
Name _______________
(Please use BLOCK letters)
4. (a) Below are pictured three long straight wires oriented perpendicular to the page. The wires
carry currents of 1.0 A, 2.0 A, and 3.0 A in the directions indicated. Also shown are three
imaginary paths around which the circulation integral
is to be calculated. Calculate the value (including sign) of the circulation integral for each of the
three paths.
B@dl
n
Loop 2
Path 1:
Loop 3
2A
Path 2:
1A
Loop 1
Path 3:
(b) In an entirely different region of space the magnetic field is given by
B = (5.00 T/m) y i
as shown in the figure below.
(i) What is the magnitude and direction of the B-field at the point with xy-coordinates
(0, 5.00 cm)?
(ii) Calculate the value of
b
ma
B@dl'
mb
B@dl'
mc
d
B@dl'
md
B@dl'
(iii) What is the value of
c
a
n
B@dl
(iv) What total current must be passing through the loop?
3A