PHYSICS EXPERIMENTS — 133
Current Balance-1
Current Balance – Warm Up
1. Force between current-carrying wires
Wire 1 has a length L (where L is "long") and carries a current I0. What is the magnitude of the magnetic
field a distance R from the wire? Give your answer in terms of the variables given and constants.
Bwire 1 (d  R)  _______________

Draw the direction of the magnetic field due to the wire at the dot () for each of the two views below.
Side View
End View
R
R
I0
wire 1
wire 1
L
Another identical wire with current I0 is placed a distance R above wire 1.

On the picture below, indicate the direction of the magnetic field at the position of wire 2.
Side View
End View
I0
wire 2
wire 2
R
R
I0
wire 1
wire 1
L
Write down the magnitude of the magnetic field experienced by wire 2 in terms of the variables given and
constants?
Bexp erienced by wire 2  _______________
On each of the above pictures, indicate the direction of the force exerted on wire 2.
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11-2

PHYSICS EXPERIMENTS — 132
Calculate the magnitude of the force exerted on wire 2. Give you answer in terms of the variables given
and constants. Show your work.
Fon wire 2  _______________
2. A different arrangement
Two identical wires (wire 1 and wire 2), each having a length L and mass mw are connected by
springs. Wire 1 is attached to a table so that wire 2 sits off the table as shown below.
Side View
End View
L
wire 2
wire 2
R
R
wire 1
wire 1
Situation 1: Equilibrium (no current)
When there is no current in the wires and the top wire is in equilibrium, wire 2 is a distance R above wire 1
as shown.
 Determine the force the spring exerts on wire 2 in terms of known variables and constants. Justify your
work.
Fspring on wire 2 (y  R)  _______________
PHYSICS EXPERIMENTS — 133
Current Balance-3
Situation 2: Mass added (no current)
A small block (mass M) is placed on top of wire 2 compressing the spring so that the distance between the
wires is now b.
Side View
End View
M
M
wire 2
R
wire 2
R
b
b
wire 1
wire 1
L
Determine the force the spring exerts on wire 2 in terms of known variables and constants. Justify your
work.
Fspring on wire 2 (y  b)  _______________
Situation 3: Mass added (current)
The small block (mass M) is left on top of wire 2, but now the current is turned on in each of the
wires so that wire 2 moves back to its original equilibrium position at y = R.
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PHYSICS EXPERIMENTS — 132
Side View
End View
M
M
I0
wire 2
wire 2
R
R
I0
wire 1
wire 1
L
What is the total force on wire 2? What is the force the spring exerts on wire 2 in terms of given variables
and constants? Explain this.
Fspring on wire 2 (y  R)  _______________
Determine the current I0 through the wires in terms of known variables and constants. Justify your work.
I 0 (y  R)  _______________
STOP! Check this result with your instructor before proceeding.
3. An "experiment"
A student takes the previous arrangement and measures that at equilibrium R = 4 mm and the length
of the wires is 25 cm.
The student places 3 mg on wire 2 and turns up the current to bring wire 2 back to its equilibrium position at
R = 4 mm. The student adds another 3 mg to wire 2 and turns the current up more to bring wire 2 back to its
equilibrium position at R = 4 mm. The student repeats this a number of times and gathers the following data.
Added mass
(mg)
Total mass added
(mg)
0
0
Distance between
wires
(mm)
4
3
3
4
3
6
4
I
(A)
PHYSICS EXPERIMENTS — 133
Current Balance-5
3
9
4
3
12
4
3
15
4
Complete the table by calculating the current in the wire for each total mass. Careful with units!
Stop! Check the entries in your table with your instructor.
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PHYSICS EXPERIMENTS — 132
Current Balance
GOAL.
 To measure the magnetic force between two wires.
 To experimentally determine the permeability constant, 0 .
 To determine the mass of an unknown.
EQUIPMENT.

 Current balance with laser
 Fractional gram mass set
 micrometer caliper
 variable transformer
 step-down transformer with rated output of 20 amperes at 6 volts
 AC voltmeter

WARNING: Laser light can damage the retina. Keep the laser level at all times to
avoid shining the light into an eye either directly or from a reflecting surface.
Note: The apparatus is very sensitive and is easily damaged, handle with care.
In this lab we will use a current balance to determine the permeability constant. To do this we are
going to use a procedure similar to that analyzed in the Warm-up activity. The current balance consists of a
long fixed conducting bar and a parallel movable bar a few
millimeters above it. The movable bar is part of a rigid frame
balanced on knife edges (the counter-balance acts like the
spring in the warm-up); see Figure 1.
The same current passes through the fixed and
movable bars in opposite directions causing a repulsive
magnetic force. We will measure the equilibrium position.
Then we will add mass which will move the wire away from
equilibrium. Then we will increase the current until the wire
moves back to its equilibrium position.
counter-balance
moveable wire
knif e-edge
fi xed wire
Fig. 1 End vie w of current balance
Q1. With a carefully drawn diagram show why two parallel wires with currents in opposite
directions experience a repulsive force. (Use answer sheet at the end.)
You found in the Warm-up that the current in the wire, I, was related to the mass added to the wire, M, the
length of the wire, L, the distance between the wires in equilibrium, R, and the permeability constant, 0 ,
I
(1)
2RMg
.
0 L

The added mass is easy to measure. The distance between the wires is a little more difficult because the
distances are so small and we cannot just grab this sensitive apparatus and use a ruler.

PHYSICS EXPERIMENTS — 133
Current Balance—7
The movement of the upper bar is magnified by the use of a moving mirror that reflects a laser beam onto a
piece of paper on the wall; see Figure 2.
The distance between wires when in equilibrium is R,
as measured from center to center. Using similar
triangles we can find the separation, s, of the bars of
the current balance:
(2)
s D/2
AD
or s 
,

A
B
2B
where A is the distance from the moving bar to the
knife edges, B is the distance from the mirror to the
 difference between the equilibrium
wall,and D is the
and touching positions of the laser beam on the wall.
You also need d, the diameter of the bars (requires
using a micrometer to measure). Adding d to the value
of s calculated from Eqn. (2) gives R, the equilibrium
center-to-center distance between the bars:
(3)
R = d + AD/2B.
I. Measuring the equilibrium distance between the bars
Initial adjustment of the apparatus
Measure the diameter of the current-carrying wire. Adjust the leveling screws so that the whole balance
rests firmly on the table. Adjust the counterpoise (counterbalancing mass) behind the mirror until the frame
oscillates freely and comes to rest with the upper bar about 1 millimeter above and parallel to the fixed bar.
Adjust the counterpoise below the mirror until the period of oscillation is 1 to 2 seconds. It should come to
rest in about 10 seconds when the poles of the damping magnets are about 2 mm apart.
Place enough mass on the scale pan so that the bars are in contact (the amount of mass is not important).
Carefully align the two bars one above the other; thumbscrews on each post permit either end of the lower
bar to be raised or lowered. Similar thumbscrews on the rear of each block permit either end of the upper bar
to be moved forward or backward. If the bars are not straight, call this to the attention of your instructor.
Determining R, the equilibrium center-to-center distance
Your current balance is now in adjustment, with the two bars in contact. They are held together due to
the mass placed on earlier. Adjust the laser so that its reflection off the mirror is visible on a wall about 2 or
3 meters from the mirror. Tape some paper on the wall at that location and mark the position of the laser
spot with bars in contact.
Now remove the mass from the weight pan and wait for the oscillations to stop. Mark this "equilibrium"
position on the wall (engage the beam lift gently and release it to make sure that the new rest point is
reproducible). The difference in spot positions between "bars in contact" and "bars without added mass in
equilibrium" is the distance D shown in Figure 1. Using equation (3) determine R (the center-to-center
distance), this only needs to be done once provided you don't jostle your apparatus.
Current Balance —8

Put the relevant values for the physical quantities in Table 1.
PHYSICS EXPERIMENTS—133
PHYSICS EXPERIMENTS — 133
Current Balance—9
II. Measuring the current
1. Connect the circuit as shown in Figure 3 for
AC operation. The current is measured using
a shunt (a known resistance) and a voltmeter
V (be sure it is in AC mode). The shunt is
made so that 1.0 A corresponds 1.0 mV.
The current through the bars will be
measured with the shunt/voltmeter.
L
V
115 V
A
shunt
AC
variable
transformer
current
balance
stepdown
transformer
Fig. 3. Circui t schematic.
2. Start with the bars in the equilibrium position you found above (about 1 mm apart with no current
and no added mass).
3. Add 20 mg to the weight pan. (If necessary, each time a mass is added or removed use the bar lift
mechanism because of the likelihood of jarring the bar and shifting the knife edges on their bearing
posts. Operate the lift mechanism very carefully while raising and lowering the bar.)
4. After adding the 20 mg mass, increase the current by closing the switch until the spot on the wall
indicates that the beam has returned to its equilibrium position.
5. Determine the current using the shunt/voltmeter. Be sure you are in AC mode! Do not keep the
switch closed.
6. Record this combination of added mass and current. (Careful with units!)
7. Repeat, using successive 20 mg increments in mass, but do not exceed the maximum current
allowed by the apparatus, roughly 10 A. Usually this means Mtotal < 150 mg. If you did not get at
least 10 points before reaching the limit of 10 A, go back and fill in using other masses.
8. Remove the added mass, but do not jostle or modify the apparatus.
9. We now have experimental data relating current and added mass.
10. Look at Equation 1 and notice that, if it correctly describes our experiment, a plot of I 2 vs. M should
be a straight line. Make this plot using your data and find the best-fit line.
III. Finding the permeability constant.


11. Look at Equation 1 and, assuming a plot of I 2 vs. M , find a symbolic expression for the slope?
Q2. What is the expression for the slope when you plot I2 vs. M?


12. From your best-fit line through the data determine the experimental slope.
13. Now calculate the permeability constant, 0 .
14. Print out your graph.
Q3. What is your experimentally determined value for the permeability constant? What is
 your value and the accepted value?
the percent difference between
IV. Determining the mass of an unknown.
15. Obtain an unknown mass from your instructor and record its identifying label.
16. Place the unknown on the current balance and adjust the current until the balance is in equilibrium.
17. Record this current.
18. Using your plot of I 2 vs. M and I you just measured, determine the mass of the unknown.


Current Balance —10
PHYSICS EXPERIMENTS—133
Q4. Record the label and your determination of the unknown mass.
PHYSICS EXPERIMENTS — 133
Current Balance—11
NAME:______________________________
COURSE/SECTION:__________________
REPORT.
d
A
D
B
R
Table 1. Relevant physical quantities.
ANSWERS TO QUESTIONS (Q1-4).