Ball-Bearing Motor

The discovery/invention of the ball-bearing motor is attributed to Milroy [1]. It has been discussed several times, with conflicting explanations [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]. This solution is a much simplified version of that given in [7]. Because the motor is weak, it is helpful to reduce friction on the axle by connecting the high-current lead to the outer races of the ball bearings, as shown above. However, I believe that this is not required in principle, and that it is simpler to analyze the interaction of a rotating, current-carrying axle with a single roller bearing whose axis is fixed, as shown on the next page. The axle has angular velocity Ω, and the angular velocity ω = −(a/b)Ω of the roller has the opposite sign, where a and b are the radii of the axle and bearing, respectively. The axial current Ia in the axle generates azimuthal magnetic field Ba. The Lorentz force vb ×Ba = (ω × rb)×Ba on the conduction electrons in the roller leads to a current Ib that Numerous videos of variants of this device are available on YouTube. The axle could be either a hollow conductor or a solid conductor. In practice, the roller (or ball) bearings are encased in a “race” that can rotate with respect to both the axle and the outer sleeve. Then, the axes of the roller bearings move azimuthally, which complicates the motion, but which does not change the essence of the analysis given below.