Improving Ampere’s Rotating Conductor through COMSOL

Ryan Yu | 8/12/25

In 1821, Ampère achieved a groundbreaking feat by creating the Rotating Conductor. Over the next two centuries, his invention was buried under a torrent of scientific discoveries—many of which laid the foundation of our modern world. But his device never received the place in history it deserves.

On July 9th, 2025, we physically recreated his conductor and tested it in Princeton’s microprocessor lab. As I watched the copper arms slowly rotate, accompanied by the cinematic hiss of sulfuric acid, I felt satisfaction—and a spark of the same excitement that Ampère himself must have experienced. From that moment on, I became captivated by a new question: How can we improve this device? Having confirmed its physics in simulation, I now set my sights on quantifying and optimizing the rotational velocity through COMSOL simulations.

In my investigation, I decided not to alter the fundamental design of the device. For example, one way to maximize the Lorentz force, and thus rotational velocity, would be by soldering another zinc ring to the conductor, increasing the current flowing through the arm. However, Ampere’s original device only had one zinc ring.

Instead I decided to experiment with magnet placement, and determining a spot for the magnet where it would exert the greatest net torque on the rotator.

This led to my abstracted workflow, each of which represents a distinct COMSOL simulation. You can see the follow-through in each Part by clicking on the bolded links:

Part I: Confirmation of Current

The Zn-Cu galvanic cell is modeled with an external short representing the rotator arch. The reactions occurring in each “half-cell” (although in the same acid bath), as well as the properties of the metals and acid are defined. COMSOL determines determine the exact current running through the arch. (We measured roughly .5 A in the physical experiment, and this step is to corroborate).

Part II: Optimization of Magnet Orientation

The current found in Part 1 is imposed through the wire for the duration of the device’s operation. The Lorentz force is derived by COMSOL in each of 12 crossovers with 4 magnet orientations and 3 arch positions. These data are analyzed to determine the optimal magnet orientation for each position that will maximize rotational velocity.

Part III: Estimation of Fluid Drag

The optimized rotational velocity found in Part 2 is imposed on the zinc ring submerged in acid. The shear rate is computed by COMSOL, and manual calculations relate this and other values to shear stress and Force. Resistance by the fluid to the rotation is one of the sources of experimental uncertainty (others include Back EMF, ion depletion in the galvanic cell & friction at the pivot).

Our previous record for continuous rotation was 3 minutes and 21 seconds. My hope is that with a smarter approach, we could achieve continuous rotation for to 5 minutes.

Conclusion

After following the workflow outlined above, I can conclude this magnet orientation sequence is optimal, and will produce a maximum angular acceleration of ≈.89 rad/sec^2.