I'm currently developing a Simulink model for the attitude control system (ACS) of an undergrad-developed CubeSat. The ACS uses magnetorquers for attitude actuation.
The magnetorquers are iron-nickel core solenoids, single-wound. Given the core permeability, number of turns, and current, how do I calculate the magnetic moment? From Wikipedia, I know that for an air-core solenoid the magnetic moment is just:
$$ \boldsymbol{\mu}=N I \mathbf{S} $$
Where $\boldsymbol{\mu}$ is the magnetic moment, N is the number of turns, I is the current, and $\mathbf{S}$ is the vector cross-sectional area of the solenoid. From that, the torque is simply $\boldsymbol{\mu}\times \boldsymbol{B}$ for my Simulink simulation (I already have the World Magnetic Map in Simulink which gives me the local magnetic field vector for any point in the orbit). This only needs to be an order-of-magnitude estimate for simulation purposes - I can measure the exact moment from the physical coils on a torsion balance later on.