Magnetic Force Balance
Equipment:
Magnetic Force Balance apparatus
High-current power supply (when needed in Part B)
banana leads (enough for redundant wiring)
Vernier caliper and Ruler
Vertical Meter-Stick Stand
Introduction:
Two parallel wires carrying current can either attract or repel one another depending on the
direction of the currents in the wires. The interaction force can be calculated using the ILB
product where I is the size of the current in each wire, L is the length of the wires, and B is
the size of the magnetic field at one of the wires due to the current flowing in the other wire.
A. Pre-lab Exercises
For this set of questions we have two 55cm long narrow-gauge wires parallel to one another.
The wires are both horizontal to the ground and one wire is 2mm above the other (measured
center-to-center). Each wire carries a current of 9.0amperes and the currents flow in opposite
directions.
A1) Make a section-view diagram of the wires where the bottom wire carries a current out of
the page and the top wire makes a current into the page.
A2) Draw magnetic field lines on your diagram that are due to the bottom wire. What is the
direction of the magnetic field at the top wire location due to the current in the bottom
wire?___________
A3) Explain why the direction of the magnetic force on the top wire is upwards.
A4) Explain why the direction of the magnetic force on the bottom wire is downwards.
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A5) Calculate the size of the magnetic field at the top wire due to the current in the bottom
wire. Show formula, calculation, and units.
A6) Calculate the size of the magnetic force on the top wire. Show formula, calculation, and
units.
A7) If we wanted the top wire to float in equilibrium above the bottom wire (assumed fixed
in place) what should the mass of the top wire in grams be? Show formula, calculation, and
units.
A8) What mass would have to be added to the top wire to maintain equilibrium if the current
in each wire were increased to 12amperes? Show formula, calculation, and units.
A9) Show that 30mg (milligrams) = 30x10-6 kg using a unit conversion table explicitly
showing the conversion.
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B. Experiment
Safety: Never look into the laser beam. Do not shine the laser above horizontal or
towards anyone else. Ask you instructor for help when required.
This experiment is performed with two horizontal wires the top one being in equilibrium at a
constant separation distance from the bottom wire. Your top wire will be in equilibrium
when no current is flowing in the wires. As current is introduced into the wires the top wire
will move upwards and you will have to add mass to make it return to equilibrium. You will
maintain the constant separation distance by adjusting both the amount of mass added to the
top wire and by adjusting the current flowing in the wires. The added weight will equal the
magnetic force when the system has returned to the equilibrium position. To calculate and
know what the equilibrium position and wire-separation distance are you will reflect a laser
beam off a mirror attached to the rotating assembly holding the top wire.
B1) Use a diagram to explain why when the mirror rotates an angle , that the laser beam
rotates through an angle 2.
Fix the rotating assembly so that the top wire is directly above the bottom wire by a distance
of just a few millimeters and that the assembly can rotate freely.
With the preceding accomplished, turn on the laser and level it so that it strikes the mirror
and is reflected on the vertical meter stick.
B1) Add a small object such as an eraser to the top assembly. Note the position on the meter
stick where the light shines.
y-closed = _____________m
B2) Take off the object and allow the assembly to reach equilibrium. Record the position on
the meter stick where the light shines.
y-equilibrium = _______________m
y = | (y-closed) – (y-equilibrium) | = ________________m
B3) Use y = (mirror-meterstick)(2)(gap/lever-arm), where “gap” refers to the distance
separating the wires, to calculate the gap.
gap = ________________meters
B4) The distance between wire centers is given by gap+wire-diameter. Measure the wirediameter and calculate the center-to-center distance, gap + diameter.
wire-diameter = ____________m gap+diameter = ________________m
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Wire the apparatus so that a direct current may be applied to cause oppositely directed
currents in the wires. Do Not Connect the Power Supply. Ask an instructor to check your
wiring.
When your circuit is checked, apply a current of about 4 amperes. The laser beam should
move above the equilibrium position. Add a mass of 30mg. Adjust the current (Never
Exceeding 10A) until the apparatus has returned to the equilibrium position. Record the
current below. Turn down the power supply as soon as you get data.
B5) Current I = __________amperes, when mass 30mg has been added.
TURN THE POWER SUPPLY TO ZERO AMPERES
In the condition above the added weight, W = I(current-length)B,
where B = oI/2(gap+diameter), or W = (I)(current-length)(oI)/2(gap+diameter)
B6) Show that the weight W of 30mg (30milligrams) is 2.94x10-4 N. Show formula and
calculation.
B7) Use W = (I)(current-length)(oI)/2(gap+diameter) to solve for o.
B8) Write your value of o from the previous question in terms of 10-7.
B9) Calculate the percent error of your value of o from the true value of o using:
% Error 
otrue  oexp erimental
otrue
 100% = ___________%
Repeat, slightly varying the mass and current until you achieve %Error < 20%.
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