# Problem no. 3 "Magic Motor"

The following sketch was added to the formulation of the task to avoid any misunderstandings concerning the experimental setup:  Before we start let us consider how a "normal" DC motor (with a commutator) works. The commutator reverses the direction of the current in the coil every half period. So all the acting electro-magnetic forces accelerate the motor. Only in two moments of the period the current is interrupted so that it can be reversed. During this time the motor continues to move due to its moment of inertia. Furthermore these two moments are very short. But the point is that the motor can work only because the current is reversed every half period. If the current was not reversed, for half of the period the acting forces would brake the motor instead of accelerating it.

Now let us consider our experimental setup. We have a coil with an electric current in a magnetic field. Obviously we have the so-called "Lorentz force" acting. The Lorentz force is a force on moving charges in a magnetic field. The Lorentz force vector is the cross-product vector of the velocity vector of the moving charge (current vector in our case) and the magnetic field vector. So the direction of the Lorentz force is rectangular on the current direction and the magnetic field.
The following sketches show the acting Lorentz forces in several points of one period:

Sketch 1 (Neutral Position 1)
Sketch 2 (Acceleration Phase)
Sketch 3 (Maximum Acceleration)
Sketch 4 (Acceleration diminishes)
Sketch 5 (Neutral Position 2)
Sketch 6 (Braking Phase)
Sketch 7 (Maximum braking forces)
Sketch 8 (Braking forces diminish)

As we can see from these diagrams half of the period is "active" and accelerates the motor, half of the period is "resistant" and brakes the motor.
The problem is that the accelerating forces and the braking forces are equal. So we can state that it is absolutely impossible that this DC motor runs without a commutator.
In fact, however, the experiment shows that the motor does work. So there must be some kind of "hidden commutator". We found out that the motor regularly loses contact. So during the braking phase there is no current so there are no braking forces. That's what we consider "hidden commutator". In order to prove this fact we did two things:

First we constructed a motor, which could no so easily lose contact. The result was that the motor ran much slowlier and changed its direction a few times. Then we ensured a permanent contact (using electrolytes) and the motor didn't run any more. It started to oscillate but it did not manage to do a full turn.

Then we went back to our original experimental setup and, using a memory oscilloscope, we plotted the current versus time during the motor was running.
The diagrams proved that during half of the period the motor had no contact so that there was actually no current. Interruptions occur also during the accelerating phase but these ones only diminish the power of the motor.
The first diagram shows one and a half period zoomed (braking phase - active phase - braking phase). The next diagrams show more periods. There one can see that the frequency increases with the voltage (more turns during the same time [1 s]), because a higher voltage causes a higher Lorentz force which causes a higher torque which causes a higher angular velocity.

Diagram 1
Diagram 2
Diagram 3
Diagram 4