Magnetic Ohm's Law (Hopkinson's Law): $\mathcal{F} = \Phi \cdot \mathcal{R}$

Where Magnetomotive Force (MMF) $\mathcal{F} = N \cdot I$

Reluctance ($\mathcal{R}$): Resistance to magnetic flux.

• Core Reluctance: $\mathcal{R}_c = rac{l_e}{\mu_0 \mu_r A_e}$
• Gap Reluctance: $\mathcal{R}_g = rac{l_g}{\mu_0 A_e}$ (ignoring fringing flux for small gaps)
• Total Reluctance: $\mathcal{R}_{tot} = \mathcal{R}_c + \mathcal{R}_g$

Inductance ($L$) & Flux Density ($B$):

• $L = rac{N^2}{\mathcal{R}_{tot}} = A_L \cdot N^2$
• $B = rac{\Phi}{A_e} = rac{L \cdot I}{N \cdot A_e}$