Magnetic reluctance - Aetherwisp

The magnetic reluctance $\mathcal{R}$ is the magnetic analog of the electrical resistance, as used in magnetic circuits. It represents resistance against magnetic flux, just like how electrical resistance represent resistance against electric current. It is measured in inverse henries, $\text{H}^{-1}$ . The reluctance of a uniform magnetic circuit of cross section $A$ , length $l$ , permeability $\mu_{r}$ is

\mathcal{R}=\frac{l}{\mu_{0}\mu_{r} A}

where $\mu_{0}$ is the Vacuum permeability.

Reluctances in series sum:

\mathcal{R}_\text{series}=\mathcal{R}_{1}+\mathcal{R}_{2}

Reluctances in parallel sum their reciprocals:

\frac{1}{\mathcal{R}_\text{parallel}}=\frac{1}{\mathcal{R}_{1}}+ \frac{1}{\mathcal{R}_{2}}

The key difference between the reluctance and resistance is that reluctances do not cause dissipation of energy. There is no "magnetic Joule effect", so to speak. As such, the analogy between the two should not be used when discussing energy conservation.