5H40.15 Interacting Coils
Abstract
Moving charges create magnetic fields. When current flows through a wire, circular magnetic field lines
perpendicular to the wire are created. Current flowing through a coil creates magnetic field lines that pass straight
through the center of the coil, perpendicular to the coil, and curved field lines elsewhere. Since a current-carrying
coil is a magnetic dipole, two coils placed next to each other will experience forces of attraction or repulsion. If
the currents in the two coils are flowing in the same direction, attraction occurs. For opposite currents, repulsion
occurs.
Picture
Setup
Setup is 0 minutes.
Safety Concerns
None.
Equipment
• Interacting Coils Apparatus
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Procedure
Use the leveling screws to ensure the coils do not slide when there is no current traversing them. There is a
level on the center of the apparatus to aid in this task. Turn both power switches on to demonstrate attraction
or repulsion. Changing the polarity switch will change the direction of current flow. If the coils have the same
polarity, repulsion between the two coils occurs. If the coils have opposite polarity, attraction occurs.
Use power cords to secure coils for transport and storage.
Theory
Moving charges create magnetic fields. The direction of the magnetic field created by a moving charge at a
given point in time and space must be perpendicular to both the velocity vector of the moving charge and the
position vector extending from the charge to the point.
In the case of a wire loop, the field lines are seen easily with the right hand rule. If the fingers are curled in
the direction of the current flow around the loop, the thumb points in the direction of the field lines at the center
of the loop. Field lines at points not passing through the center of the loop are also found by the right hand rule.
If the thumb is now pointed in the direction of current flow, the fingers curl in the direction of the field lines.
These field lines form tighter curves near the wire, as seen at the top and bottom of Figure 1.
Current Carrying
Loop
S
N
Figure 1: Diagram showing the magnetic field lines surrounding a current carrying loop.
A coil comprises many tightly wound current loops, and the geometry of the field lines for a coil and a loop are
the same. The field lines passing through the center of the loops in a coil are superimposed so the field strength
at the center of the coil increases.
Notice that a loop, and thus, a coil exhibits the field lines of a magnetic dipole. By convention, the side
of the coil from which field lines emerge is the north pole, while the side in which field lines enter is the south
pole. Since a current-carrying coil is a dipole, two freely moving current-carrying coils either attract or repel each
other. If current is flowing in the same direction in both coils, then the opposite poles from each coil are facing
each other and the coils attract. If the loops have current flowing in opposite directions, repulsion occurs.
It is possible to approximate the magnitude of the force between two current-carrying coils. If the force
between non-parallel parts in the two coils is ignored, the two coils can be treated like a system of two parallel
wires. Consider the magnetic field strength of a current-carrying wire,
B=
µ0 I
,
2πd
2
(1)
where B is the magnetic field strength, I is the current running through the solenoid, d is the perpendicular
distance from the wire to the point where the field strength is being measured, and µ0 (µ0 = 4π × 10−7 T m/A)
is the permeability of free space. A current-carrying wire in an external magnetic field experiences a force,
→
− →
→
−
−
F = I l × B,
(2)
→
−
→
−
where F is the force, I is the current in the wire, l is a vector equal to the length of the wire in the direction
→
−
of the current flow, and B is the external magnetic field.
In the case of two parallel current-carrying wires, the magnitude of the force exerted on the second wire by
the magnetic field due to the first wire is
→
− −
−→
→
F12 = I2 l × B1 ,
(3)
−→
where F12 is the force on the second wire due to the first wire, I2 is the current flowing through the second wire,
and B1 is the magnetic field of the first wire. The magnitude of this force is found by substituting Equation 1
into Equation 3 to yield,
µ0 lI2 I1
,
(4)
F12 =
2πd12
where d12 is the distance between the two wires. The magnitude of the force on the first wire by the second wire
is equal to the force on the second wire by the first wire.
Equation 4 is adjusted and used to approximate the magnitude of the force between two coils. The length of
a coil is approximated by the circumference of a loop in the coil
l = 2πR,
(5)
where R is the radius of the loop. If the first coil has N1 turns and the second coil has N2 turns, the currents
flowing through the first and second coils increase respectively by these factors.
Substituting Equation 5 into Equation 4 and correcting for the current terms, the force between the two coils
is approximated to be,
N1 N2 µ0 RI2 I1
.
(6)
F =
d12
The apparatus used in this demonstration comprises coils of 1000 turns each and radius 12.2 cm. When the
power supplies are turned on, a current of approximately 0.751A flows through the coils. A theoretical plot of
force between the two coils for various distances of separation is shown in Figure 2.
Figure 2: Graph showing the theoretical force bettween the two coils for various distances of separation with
approximately 0.751A flowing through the coils. magnetic field lines surrounding a current carrying solenoid.
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References
[1] Knight, Randall D. Physics for Scientists and Engineers, ”Magnetic Forces on Current-Carrying Wires” 2nd
ed, Calfornia: Pearson Addison-Wesley, 2008. pg 1024-1026.
[2] others. ocw.mit.edu/courses/physics/8-02t-electricity-and-magnetism-spring-2005/labs/exp08.pdf.
[3] Knight, Randall D. Physics for Scientists and Engineers, ”The Magnetic Field of a Current”, 2nd ed, California:
Pearson Addison-Wesley, 2008. pg 1005-1009.
[4] Sutton, Richard Manliffe. Demonstration Experiments in Physics, ”E-148/149. Forces on Parallel Conductors”,
McGraw-Hill Book Company Inc, New York and London, 1938. pg 310-311.
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