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MAGNETIC FORCE BETWEEN PARALLEL CURRENTS
References
Crummett and Western Physics: Models and Applications, Sec. 28-2, 29-1,2
Halliday, Resnick, and Walker, Fundamentals of Physics (5th ed.), Sec. 30-2
Tipler, Physics for Scientists and Engineers (3rd ed.), Sec. 25-3
Introduction:
Electric current — moving charge —
creates a magnetic field. In particular, a
current in a long straight wire sets up a
magnetic field B whose direction at any
point is tangent to a circle drawn around
the wire. Fig. 1 illustrates this. The
direction of B obeys a right-hand rule: if
you point the thumb of your right hand
along the current direction, its curled
fingers indicate the direction of the field
lines around the wire. The magnitude
of B in this case is given by
B= 2 K
I
d
(1)
(1)
Figure 1
Magnetic field lines for a straight
where B is the field at distance d from a
wire
wire carrying current I. The constant K
depends on the units in which the other quantities are expressed.
It is also true that a current-carrying wire placed in an external magnetic field will experience a force
due to the field. If the current is perpendicular to the magnetic field direction, the force is perpendicular
to both, and has magnitude
F=I LB
(2)
where L is the length of the wire and I the current in it. The force direction follows from another
right-hand rule: if the fingers of the right hand are curled from the direction of I into the direction of B,
then the thumb points in the direction of the force.
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MAGNETIC FORCE BETWEEN PARALLEL CURRENTS
It follows that two current-carrying
wires exert magnetic forces on one
another. In Fig. 2, current I1 is the
source of a magnetic field at the
position of I2; the field exerts a force on
I1. (Wire 2 exerts an equal and
opposite force on wire 1.) From
Equations (1) and (2), the force must
be given by
F = 2K
L
I1 I2
d
(3)
The SI unit of electric current, the
ampere, is DEFINED by saying that the
Figure 2
Force between parallel
constant K has the value 10-7 N/A2.
currents
Thus if the same current I is passed
through two parallel wires, the force they exert on one another has the form
F =C I2
with
C=
2K L
L
= (2 x 10-7 N/ A2 )
d
d
(4)
In this experiment you will use a current balance to verify the I2 dependence and check the value of
the constant C predicted by Equation (4).
Equipment
current balance
DC power supply
double pole double throw (DPDT) reversing switch
ammeter (0-10 A)
laser
leads
plastic spacers
Procedure
The current balance is sketched in Fig. 3 (top of next page). One of the two wires is part of a
frame which balances on a knife-edge. The distance d between the centers of the two wires at
equilibrium can be adjusted by moving the counterweight. Once a value of d is set, a small weight is
placed on the pan and the movement of the balance is observed with an optical-lever arrangement.
MAGNETIC FORCE BETWEEN PARALLEL CURRENTS
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Current to the wires is then
turned on and adjusted
until the original balance
position is restored; so you
have determined how
much current in the wires
is required to balance a
known weight.
CAUTION: it is not hard to
Figure 3
The current balance
damage the knife edges,
so consult your lab
instructor about proper procedures for adjusting and using this instrument before you get started. The
sensitivity of the balance should be adjusted so that the heaviest weight to be used (probably 40 or 50
mg) moves the arm down a distance slightly less than d, so that the wires will not come into contact.
(1)
Set up the circuit shown in Fig. 4. Have your instructor check it before you
plug it in. Note that the maximum current rating of the power supply is 10 A, and it will be
necessary to use currents almost that high in the experiment; so you will have to use care in
adjusting the current.
(2)
Position the laser, as indicated in Fig. 3, so that its beam falls on the wall (after reflecting from the
mirror) at a convenient height. Mount a piece of graph paper on the corkboard provided on the
wall so that the laser beam falls on it, to use as a scale.
Figure 4
(3)
Experimental circuit
Measure the length L of the parallel wires and the diameter of the wire. Record them along with
their uncertainties. It is important to
set an appropriate starting separation between the wires. Plastic spacers will be provided to aid
in setting this distance. Measure three or four of these spacers together and divide to find the
thickness of a single spacer. Estimate the uncertainty in the spacer thickness. Gently place a
spacer between the parallel wires and hold them together with very light pressure. Mark the
location of the reflected laser spot on the wall. Now remove the spacer and carefully adjust the
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MAGNETIC FORCE BETWEEN PARALLEL CURRENTS
position of the counterweight on the apparatus until the laser spot returns to the location you
marked. This indicates that the wire spacing is again what it was with the spacer between the
wires. From the spacer thickness and the wire diameter calculate d, the center to center
separation of the parallel wires.
(4)
Place a 5 mg weight on the pan, and allow the balance to come to rest at its new equilibrium
position. Then turn on the current, and adjust it to restore the original equilibrium position of the
balance. Turn the current back to zero, and repeat this procedure several times to obtain an
average value of I required to balance the added weight.
Now reverse the current in the wires by turning the power supply to “standby” and reversing the
position of the DPDT switch, and repeat the entire procedure. Find the overall average value for
the current from both current directions.
(5)
Increase the mass on the pan in steps of 5 mg and continue repeating procedure (4) until the
balancing current reaches nearly 10A.
(6)
Increase the equilibrium value of the wire separation by using two plastic spacers instead of one
as you did in step three above. Repeat the procedure of steps (4) and (5) above for the new
spacing, but use 10 mg weight increments in lieu of 5 mg.
Analysis
For each value of the weight in the balance pan, calculate the force (mg) between the two currents at
balance, and the overall mean value of the balancing current and its standard error. Make a table of F
vs. I for each of the values of d. For each value of d, draw a graph of F vs. I2, and discuss whether
your data are consistent with Equation (4). Calculate the expected value of C, from Equation (4), and
its uncertainty. Obtain an experimental value for C from the slope of the graph, together with an
estimate of its uncertainty, and compare it to the value calculated from Equation (4). Discuss whether
your results agree, within experimental errors, to what is expected from (4).
The reason for reversing the current and averaging the balancing currents you observe in both
directions is to cancel out the effects of the earth's magnetic field. Explain how this works.
Magnetic force between parallel currents.doc
last update 6/2002, MJM and MMS