Magnetic Force on a Current-Carrying Conductor
Department of Physics & Astronomy
Texas Christian University, Fort Worth, TX
June 29, 2016
1
Introduction
When a wire carrying a current is placed in a uniform magnetic field a force is exerted on the wire.
This force depends on the magnitude of the current, I, the length of the wire, d, and on the relative
orientation of the wire with regard to the magnetic field, B, and can be written as
~ B|
~ sin θ,
|F~B | = I|d||
(1)
~ The direction of the force F is given by the right hand rule.
where θ is the angle between d~ and B.
When the wire is perpendicular to the magnetic field (sin θ = 1), Eq. (1) simplifies to
FB = IdB.
(2)
If we graph the force as a function of the current, we get a straight line with a slope of dB.
A schematic of the experiment is shown in Fig. 1. When a current is passed through the wire,
the magnetic force will cause the wire to deflect from the vertical. When the wire is balanced,
all forces are in equilibrium. There are three forces acting on the wire: the force of gravity pulls
straight down; the tension pulls along the vertical part of the wire; and the magnetic force pulls
horizontally to the right. Applying Newton’s laws in the x and y directions yields the equations
T sin φ = mg
(3)
T cos φ = FB .
(4)
Dividing the two equations will eliminate T ,
tan φ =
mg
.
FB
(5)
Which gives us an expression for calculating the magnetic force
FB =
2
mg
.
tan φ
Equipment
power supplies, current-carrying wire on stand, magnets, wires, ruler
1
(6)
Figure 1: Experimental setup. A schematic (left) of the experimental setup.
2
3
Procedure
1. Measure the length and width of the magnetic poles. Make a note of how the poles are
oriented.
2. Connect the current-carrying wire to the power supply. Use the DC output and have your
TA check the wiring before you turn it on. There are four closely spaced holes in the top
beam of the stand. The hole furthest from the support hangs the wire vertically between the
poles of the magnet. The remaining three holes are 15, 30, and 45 mm from this hole. Fix
the current-carrying wire to the 15 mm hole.
3. Slowly increase the current until the wire hangs between the magnetic poles again. If your wire
does not move between the magnets or moves away from the magnets, reverse the direction
of the current. Record the current.
4. Move the current-carrying wire to the next hole and repeat the experiment and repeat the
measurement. Repeat again for the last hole.
5. Rotate the poles of the magnet so that the length of current affect by the magnetic field
changes. Repeat the measurements for all three current-carrying wire positions.
4
Report
Make sure your report includes the following:
1. Calculate the angle of deflection using the horizontal displacement of the wire and the height
of the wire (200 mm).
2. Calculate the force on the current-carrying wire using the mass of the wire (6.23 g).
3. What a graph of magnetic force as a function of the current. Draw separate lines for the two
magnetic pole positions.
4. Calculate the slopes of the two lines and use that to find the strength of the magnetic field.
Do your two calculations agree with each other? Discuss some reasons for discrepancies.
3