I am building an RL series circuit with a toroidal inductor that I am winding on my own. The toroid is made of steel (low carbon, I believe, but not 100% sure) and has about 280 turns of 22 gauge wire. The inner diameter of the toroid is 4.25 in. and the outer diameter is about 5.25 in. The resistor is 0.6 ohms. The circuit is diagrammed below.
simulate this circuit – Schematic created using CircuitLab
I know that according to Maxwell's equations, $$\mathbf{B}=\mu(\mathbf{H} + \mathbf{M})$$ where B is the magnetic flux density in Teslas, \$\mu\$ is the permeability of the material, H is the magnetic field strength in Henries/meter, and M is the magnetization of the material in Henries/meter. Note that $$\mu = \mu_0\mu_r$$ where \$\mu_0\$ is the permeability of free space and \$\mu_r\$ is the relative permeability of steel, which I take to be about 1000 at DC. I also know that, in ferromagnetic materials, permeability is a function of the frequency of the input signal as well as of the magnitude of H (link 1, link 2).
A few questions:
- How can I calculate/experimentally determine the minimum voltage/current with which I need to drive the circuit in order to saturate the magnetic flux density inside the toroid? I want to be able to run an AC signal (< 100 Hz) through my circuit for several minutes such that the magnetic field reaches saturation but without causing the circuit to overheat.
- Is it possible to apply such a high voltage/current that the relative permeability decays to 1? If so, does this mean that at very high voltages, the field wouldn't saturate since the permeability is too low?
magnetic field reaches saturation but without causing the circuit to overheat
That is slicing it thin, with contradictory results. They are not exclusive events. \$\endgroup\$