Download Magnetic Force on Current Carrying Wires

LPC Physics
Magnetic Force on Current Carrying Wires
Magnetic Force on Current Carrying Wires
Purpose:
To explore the magnetic force exerted on a current-carrying wire, and how it varies with
current, length, magnetic field and angle.
Equipment:
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Basic Current Balance and Accessory
Quadruple-Beam Gram Balance
DIGI Power Supply
DMM
Patch cords
Theory:
Magnetism is a phenomenon that has been known, if not understood, for
thousands of years. The term magnetism comes from the region of Magnesia (once a
province of Greece, now a part of Turkey) where certain stones were found that had the
property of attracting pieces of iron. These stones, called lodestones, were also known by
the Chinese who fashioned them into navigational compasses in the twelfth century. In
the late 1500’s, William Gilbert, later principal physician to Queen Elizabeth, made
artificial magnets by rubbing a lodestone against a piece of iron. He also was the first to
suggest that the Earth itself was a very large magnet, the source of the compass’s
tendency to align itself North to South. In 1750, John Michell, a geologist/astronomer
who invented the torsional balance through his study of earthquakes and who also
predicted the existence of black holes, published a treatise on magnetism in which he
showed that magnetic poles obey an inverse-square law (as does the force of gravity).
The Greeks also had an understanding of the rudiments of electrical theory. In
fact, the word electron comes from the Greek word for “amber”. Studying amber, they
found that when they rubbed it with a cloth, it was able to attract small bits of things, like
straw. The same William Gilbert discovered other materials with the strange properties
of amber...he called them “electrics”. Gilbert also defined as separate the similar
phenomena of static electrical attraction from that of magnetic attraction.
Stephen Gray, in the early 1700’s, was the first to show that the electrical attraction (or
effluvia as it was called then...electricity was considered at that time to be a fluid) may be
transmitted through an object: many objects were tried, including cork, various metals,
green vegetables, and his students. This was the first indication of an electric current.
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Stephen Gray, in 1729, discovered that the electric force, made by rubbing glass, could be sent for
long distances over a wire. The electricity could, thus, be separated from the rubbed bodies and wasn't
an exclusive property of some material. The figure shows that the electric force of a rubbed glass
could be sent, through a wire, to the body of a person. There is not a direct contact.
REF: http://www.geocities.com/SiliconValley/Circuit/1858/graye.htm
Benjamin Franklin also made great advances in the study of electricity,
particularly in linking the natural phenomenon of lightning to the small electric sparks
produced in laboratory. He is remembered in the terminology we use today; positive and
negative, plus and minus, battery, armature, charge, condensor and conductor.
In April of 1820 Hans Christian Ørsted, a professor of Physics at the
University of Copenhagen, Denmark, made an accidental discovery that
re-linked the electric and magnetic theory. One of the many stories has
it that the technician in charge of setting-up and dismantling lecture
demonstrations was slacking one day, and while he put out the
equipment for the day’s demo in magnetism, he did not remove the
electrical equipment from the previous lecture period. Ørsted attempted
to work around the electrical wires, some of which were still hooked up and had current
flowing through them. When he brought a magnetic compass near one of the live wires,
he found that the needle turned and pointed toward the wire. In further investigations, he
found that a live wire will be deflected in the presence of a magnetic field, which led the
way to the development of the electric motor. Though excited about his discoveries, he
left the further investigation of the connection between electricity and magnetism to
others, particularly one André-Marie Ampère. Ørsted went on with work in other areas
of physics and chemistry, particularly the first preparation of metallic aluminum in 1825.
You can hear a nice little song about him at the following website:
http://www.haverford.edu/physics-astro/songs/oersted.htm
Ampère made his living primarily as a professor of Mathematics, though his
interests ranged to physics, metaphysics, chemistry and poetry. In the early 1820s he
expanded on Ørsted’s discovery, able to quantify the effect, and put forth an explanation.
An electric current, he said, is the source of a magnetic field, just as an electric charge is
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the source of an electric field. The magnetic field, B, around a wire is proportional to the
current flowing through the wire, and curls around the wire according to the right-handrule. He also demonstrated that two current-carrying wires will attract or repel each other
depending on the relative directions of current. Such an experiment, of which ours is a
modification, is often called Ampère’s Experiment.
Another nice little song, this one about Ampère’s Law, can be found here:
http://www.haverford.edu/physics-astro/songs/ampere.htm
The interaction between a moving charge and a magnetic field can be described by the
force relationship:
r
r r
F = qv × B
where q is the magnitude of the moving charge, v is the velocity of the moving charge,
and B is the magnetic field. For a segment of wire of length ds carrying a current I, the
force can be derived from the relationship above by letting
dq
⇒ dq = Idt
I=
dt
ds
v=
dt
r
r
r r
r r
F = qv × B ⇒ dF = dqv × B
v
r
ds r
v r
dF = Idt × B = Ids × B
dt
This relationship can then be integrated over a given length of wire to determine the
force. If ds and B are perpendicular to each other, then a wire of length L in a magnetic
field B, experiences a force described as:
r
r r
F = IL × B
which reduces to
F = ILB
Using this relationship, it is easy to see that the SI unit of magnetic field strength, the
Tesla is related to the current (Amp) and the length of the wire (Meter) by:
1N
1T =
Amp ⋅ m
So…how are we going to measure the force on a current-carrying wire imprinted on a
circuit board, such as we have amongst our equipment? Unfortunately, there is no good
direct method (that I know of) . But luckily, the laws of Newtonian Physics you learned
long ago still apply to today’s topics! Remember specifically Newton’s Third Law:
If two bodies interact, the force exerted on body 1 by body 2 is equal
in magnitude but opposite in direction to the force exerted on body 2
by body 1.
F12 = -F21.
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Thus, if a magnetic field exerts a force on a current-carrying wire, the current-carrying
wire (or, more accurately, the B-field created by the current) exerts a force back on the
original magnetic field (or, more accurately, the magnets, current-carrying wire, or
whatever happens to be producing the magnetic field). Instead of measuring the force
exerted on the wire, we will measure the force exerted on a small bank of magnets,
knowing with full confidence that these two forces are equal in magnitude.
Still, you may ask, how are we going to measure the (presumably smallish) force exerted
by the current-carrying wire on the stack of magnets? Surely the force produced is too
small to accelerate the magnets across the table (and then we’d have to account for
friction, of course). There must be an easier way…
Hopefully, back in Physics 8A or in Physics 8C you did the experiment on Archimedes’
Principle. If not, hopefully you at least discussed it in class. Why is this applicable, you
ask? Remember that in the Archimedes lab we measured the mass (weight) of a dry
object in air, then measured the mass (weight) of that same object while submerged in
water. The mass (weight) appeared to be less when the object was submerged, right?
This is because the buoyant force exerted on the object by the water is in the upward
(opposite to gravity) direction. If we orient the magnets and wire such that the force
between them is exerted in the vertical direction, we can measure the apparent change in
mass of the magnets…either greater or smaller, depending on whether the force is
attractive or repulsive, depending upon the direction of the current through the wire.
Since we know that the mass of the magnets does not actually increase or decrease, we
can interpret this “change in mass” as a secondary force acting on the magnets. We can
determine the magnitude of the force by multiplying the change in mass, ∆m, by the
gravitational acceleration constant, g = 9.8 m/s2.
Remember: what we call your “weight” is simply the magnitude of the force of gravity
acting upon your mass:
Fg = W = mg
where g = 9.8 m s 2
Thus, we will set our bank of magnets on a gram-sensitive quadruple-beam balance. We
will suspend the circuit-board such that the printed section runs between the north and
south poles of the magnets. We will then run a current through the “wire”, exerting a
force on the magnets, and we will measure that force by:
Fmagnets = ∆m measured g = ( m no.current − mcurrent ) g .
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The theory for this lab was written by Jennifer LK Whalen
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Experiment:
current loop
main unit
lab stand
quadruple-beam
balance
Figure 1
Part A: Force vs. Current
1. Set up the apparatus as shown in Figure 1.
NOTE: You do not need to add additional resistance for this set-up to work! DO NOT
hook up a resistance box…everything is fine the way it is written.
2. Determine the mass of the magnet holder and magnets with no current flowing.
Record this value as m0.
3. Set the current to 0.5 amp. Determine the new “mass” of the magnet assembly.
Record this value as m(c).
4. Subtract m0 from m(c). Record this value as ∆m(c).
5. Repeat Steps 3 & 4, increasing the current in 0.25 amp increments until you have
reached the maximum possible current.
Part B: Force vs. Length of Wire
1. Set up the apparatus as in Figure 1.
2. With no current flowing, determine the mass of the magnet assembly. Record this
value as m0.
3. Determine the length of the conductive foil on the current loop. Record this value
as l.
4. Set the current to 2.0 amps. Determine the new “mass” of the magnet assembly.
Record this value as m(l).
5. Subtract m0 from m(l). Record this value as ∆m(l).
6. Turn the current off. Remove the current loop and replace it with another.
Repeat Steps 3-5 until you have used all available current loops.
Part C: Force vs. Magnetic Field
1. Set up the apparatus as shown in Figure 1.
2. Mount a single magnet in the center of the holder.
3. With no current flowing, determine the mass of the magnet assembly. Record this
value as m(n).
4. Set the current to 2.0 amps. Determine the new “mass” of the magnet assembly.
Record this value as m(n,c).
5. Subtract m(n) from m(n,c) and record this difference as ∆m(n).
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6. Add additional magnets, one at a time. (Make sure that all the North Poles of the
magnets are on the same side of the assembly). Each time you add a magnet,
repeat Steps 3-5.
main unit
accessory unit
lab stand
Figure 2
Part D: Force vs. Angle
1. Set up the apparatus as shown in Figure 2.
2. Determine the mass of the magnet assembly. Record this value as m0.
3. Set the angle of the accessory unit to 0o with the direction of the coil of wire
approximately parallel to the magnetic field. Set the current to 1.0 amp.
Determine the new “mass” of the magnet assembly. Record this value as m(θ).
4. Subtract m0 from m(θ) and record this difference as ∆m(θ).
5. Increase the angle in 5o increments up to 90o, and then in –5o increments to –90o.
At each angle repeat the mass/force measurement.
Analysis:
Part A: Force vs. Current
1. Multiply ∆m(c) by g to get the force acting on the magnets, F(c).
2. Plot a graph of F(c) vs. current.
3. What is the nature of the relationship between these two variables? What does
this tell us about how changes in the current will affect the force acting on a wire
that is inside a magnetic field?
4. Decide what equation governs this relationship, and use the slope of your graph to
quantitatively verify this relationship within experimental uncertainties.
Part B: Force vs. Length of Wire
1. Multiply ∆m(l) by g got get the force acting on the magnets, F(l).
2. Plot a graph of F(l) vs. l.
3. What is the nature of the relationship between these two variables? What does
this tell us about how changes in the length of a current-carrying wire will affect
the force that it feels when it is in a magnetic field?
4. Decide what equation governs this relationship, and use the slope of your graph to
quantitatively verify this relationship within experimental uncertainties.
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5. Using the slopes of the Force vs. Current and Force vs. Length of Wire, determine
a value of the magnetic field, B.
Part C: Force vs. Magnetic Field
1. Multiply ∆m(n) by g to get the force acting on the magnets, F(n).
2. Plot a graph of F(n) vs. n.
3. What is the relationship between these two variables? How does the number of
magnets affect the force between a current-carrying wire and a magnetic field?
4. Is it reasonable to assume that the strength of the magnetic field is directly
proportional to the number of magnets?
5. What would happen if one of the magnets were put into the assembly backwards,
with its north pole next to the other magnets’ south poles? If there is time, try it.
6. Decide what equation governs this relationship, and use the slope of your graph to
quantitatively verify this relationship within experimental uncertainties.
Part D: Force vs. Angle
1. Multiply ∆m(θ) by g to get the force acting on the magnets, F(θ).
2. Plot a graph of F(θ) vs. θ.
3. What is the relationship between these two variables? How do changes in the
angle between the current and the magnetic field affect the force acting between
them?
4. What angle produces the greatest force?
5. What angle produces the least force?
Length of Wire Loops
Current Loop
Length
SF 40
1.2 cm
SF 37
2.2 cm
SF 39
3.2 cm
SF 38
4.2 cm
SF 41
6.4 cm
SF 42
8.4 cm
Results:
Write at least one paragraph describing the following:
• what you expected to learn about the lab (i.e. what was the reason for conducting
the experiment?)
• your results, and what you learned from them
• Think of at least one other experiment might you perform to verify these results
• Think of at least one new question or problem that could be answered with the
physics you have learned in this laboratory, or be extrapolated from the ideas in
this laboratory.
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Clean-Up:
Before you can leave the classroom, you must clean up your equipment, and have your
instructor sign below. How you divide clean-up duties between lab members is up to you.
Clean-up involves:
• Completely dismantling the experimental setup
• Removing tape from anything you put tape on
• Drying-off any wet equipment
• Putting away equipment in proper boxes (if applicable)
• Returning equipment to proper cabinets, or to the cart at the front of the room
• Throwing away pieces of string, paper, and other detritus (i.e. your water bottles)
• Shutting down the computer
• Anything else that needs to be done to return the room to its pristine, pre lab form.
I certify that the equipment used by ________________________ has been cleaned up.
(student’s name)
______________________________ , _______________.
(instructor’s name)
(date)
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