Experiment 5: The Current Balance
Object: To see if the measured magnetic force between current carrying wires matches that
predicted by theory.
Apparatus: A current carrying bundle of wires, B2 in the diagram,
creates a magnetic field around itself. Another bundle of wires
hanging from a balance, B1, feels a force from this field, pushing the
balance upward. The device measures this force the same way a
triple beam balance works: A weight (a small wire) pushing it back
down is slid along the arm until the balance balances.
To balance, the torque from the magnetic force must equal the torque due to the weight:
(6 cm)(Fmag) = (d cm)(W)
So, the magnetic force is d/6 times the hanging weight.
Procedure: Connect the circuit as shown.
Use a low-voltage, high current power
supply with fins on the sides, not our usual
gray ones. Starting at (+) on the power
supply, current goes through the ammeter,
then through the bundle on the balance, B1,
then to the double-pole switch. With this in
one position, the current then goes straight
back to (-); in the other position, it goes
through B2 and then back to (-). So, current
passes through the B1 either way, but in one
position the magnetic field from B2 is off,
and in the other position it is on.
Check that the pointer does not rub on the scale. The counterweight, m, should be adjusted so that
the balance almost, but not quite, tips over backward. (The pointer does not have to be at 0.) A
good way to check if the balance moves freely is the blow on it: It should bob up and down a few
times. Also, check that the wires under the base run directly under the balance.
You have an approximately .2 gram wire. Measure its mass on a balance which can be read to the
nearest hundredth of a gram. To obtain its weight in newtons, convert the mass to kilograms and
multiply by 9.8. (As explained in PHY 121, mass is the amount of matter in the wire; weight is the
gravitational force on it. 9.8 m/s2 is the strength of Earth’s gravitational field.)
With the little wire off the arm, send 5.0 amps through B1 only, and note the position of the pointer.
(Check that the wires on the balance are not resting against those on the base.)
CAUTION: The needle points or other loose connections could get hot.
Set the switch for current in both sets of wires. If the pointer goes down not up, switch the current’s
direction in one set of wires. Readjust the power supply as necessary to keep the current at 5.0
amps (it tends to drop as connections heat up, increasing their resistance.) If you can’t maintain 5
amps, turn it off for a few minutes to let things cool.
Hang the wire over the arm as shown above, and move it until it has the right amount of leverage, d,
to bring the pointer back to its position with current in B1 only. The balance can stick a little. (It
doesn’t take much with such small forces.) So, there will be a range of places where the weight puts
the pointer at the right mark. Slide the weight around and find what this range is. Record dmin and
dmax, the minimum and maximum wire positions where the pointer sometimes returns to the correct
mark when gently disturbed. From these, find the maximum and minimum values for the
"measured force" using (6 cm)F = d W, as explained above.
Theoretical Force: With the pointer still in the same position (you can turn off the current and just
hold it in place), measure r, the distance between the centers of the two bundles of wires, as shown
above. A good way to do this is to measure left to left, then right to right, then average.
Also measure the length of the wires along the bottom of the balance, and count the number of
strands in both bundles. Record which setup you have from the tag on top of it. When you're done,
stick your piece of wire to the base with some scotch tape so it won't get lost.
CALCULATIONS:
1. Find the magnetic field which one wire on the base creates at the bottom of the balance.
2. Multiply this by the number of strands on the base to obtain the total field.
3. From the field, find the force on a single wire on the balance.
4. From the total number of wires, find the total force. (Ignore the other three sides of the coil on
the balance.) This is your theoretical value for the magnetic force. It could be off by as much as
20%, due especially due to the uncertainty in measuring r between the wiggly bunches of wires.
Express your answer as in this example: F = 3.0 + .6 mN. (20% of 3.0 is .6.)
In your conclusion, state whether the measured and theoretical forces agree.
PHY 122
Report on Experiment 5: The Current Balance
Hanging Mass: _______________
W = _______________
Current = 5.0 A
d max.= ______________
d min.= ______________
Determine measured force:
r = ____________________
Length of wires: ____________________
Number of strands on base: ____________________
Number of strands on balance: ____________________
Setup #: ____________________
Determine theoretical force & its uncertainty: