May 12, 2010
Los Angeles, CA
IYPT 1999 #2: Magic Motor: Construct a DC motor without a commutator,
using a single battery, a single permanent magnet, and a single piece of
wire formed into a roughly flat circular coil with multiple turns. Predict the
frequency of rotation of this motor from first principles and compare to
experiment.
I. Conceptual Picture I-1 DC motor
It is well known and described in multiple books and web sites (see for example
see references [1-2]). A loop (coil) with
electric current is placed in the magnetic
filed. The magnetic field exerts two
opposite forces on the sides of the loop
and these two forces apply torques on
the loop and the loop rotates. However,
after the loop makes a half turn, the
forces would change direction of the
torques and after several oscillations the
motor will stop (see Figure 1). To keep
the loop rotating, the DC motor uses a
split ring commutator (see the Figure
2). It switches the direction of the electric
current after each half turn and the loop
keeps rotating in the same direction.
I-2. “Magic Motor”. There is a difference between regular DC Motor and one
from the problem. The “Magic motor” does not have a commutator. Figure 3
below shows the roughly flat coil of multiple turns. There is no commutator. The
motor looks like the motor on Figures 1 and 2. So, you should not expect for
regular motion except for small oscillations. But with some adjustments for
thickness of the wire and shape you can get continuous rotation. It is magic?
You can make one using different designs: as it is on the picture on the USAYPT
web site [3], or with the magnet located on one or both sides from the coil rotor
[4], or with the magnet and the coil rotor placed on the board which is on the
table and not necessarily on top of the battery [5], or you can use your own
design. You can also purchase a motor kit in the teacher supplies stores (see, fro
example, [6]). If you make it as it is shown on the Figure 3, you will be surprised
that it spins and it spins pretty fast. The motion does not look like oscillation at all.
II. References
[1] R. A. Serway, J. S. Faughn, “Holt Physics”, 2005, Holt, Rinehart and Winston
[2] hyperphysics.phy-astr.gsu.edu/hbase/magnetic/motdc.html#c2
[3] www.usaypt.org
[4] The Physics Teacher, Vol. 47, P. 204
[5] The Physics Teacher, Vol. 39, P. 174
[6] www.arborsci.com/prod-Worlds_Simplest_Motor-691.aspx
III. Theory
Hong, Choi, and Hong [4] offered the idea of the half stripped arm of the coil rotor
(Figure 3). So, the coating on the opposite half will break the circuit and,
therefore, will act as the commutator. This motor would work and it would look
like the Magic motor, but it contains an actual commutator. Klittnick and Rickard
[5] showed that it is not important to half strip the arm. Read the article where
they describe an experiment and conclude that the coil rotor jumps during each
rotation and “the current flows through the coil only during that portion of rotation
corresponding to the time that the heavy side of the coil is at the bottom of its
swing.” See Figure 4.
IV. Experiment
Select the thickness of the copper wire so that it does not easily bend, but is not
too heavy. Use different designs to find your favorite. Reference [5] suggests
using about 15 turns in the coil. The trickiest part is to estimate the time when the
coil rotor jumps in your cradle and breaks the circuit. The result depends on the
apparatus’ design, but the reason of why the loop jumps is the same. It happens
because the center of mass of the loop is skewed from the axis of the loop’s
revolution. So, the centripetal acceleration changes direction. The loop would
loose contact to the support when the centripetal acceleration of the center of
mass would exceed the value of the acceleration due to gravity and would be
directed down. The force of normal reaction becomes equal to zero and it means
that the wire lost contact with the supporting conductor.
Good luck!
T.Bibilashvili