magnetic actuator torque calculation

Question

I would like to formulate how much load can carry for the magnetic actuator used in RC airplanes. Example photo:

It consists of a coil and a magnet. And works according to lorentz force principle.
The torque exerted by the magnetic field on the magnet is directly dependent on the strength of the magnet, the number of turns on the coil, and the current through the coil. So to increase or decrease the torque, we need to either get a better or worse magnet, wind more or less turns, or increase or decrease the current. How can formulate it? Like
Torque = current x magnet property x turn of coil
2 N.cm = 0.1mA x ? x 340 turns (numbers are only example,not real)

Answer 1

The torque is linear in the coil current and the magnet's magnetic moment, so torque = current * magnetic_moment * coil factor.

It's easy to measure the current accurately.

It's possible to track down (using your favourite search engine) an approximate formula for the field strength versus current for a coil of N turns, given the number of turns and dimensions. It's easy to measure the dimensions, it's not so easy to count the turns if you didn't wind it yourself.

It's not so easy to measure the magnetic moment of the magnet in your actuator directly, at least not in an accurate way.

With so many things being difficult to measure, it's best to simply measure the torque versus current curve for your actuator, plot the results on a graph, and fit a straight line to it for your_actuator_factor. Then use the formula torque = current * your_actuator_factor. This empirical factor sweeps up all the uncertainties / difficulties in coil dimensions, number of turns and magnetic moment.