Ohm's law for magnetic circuits states that the magnetomotive force (mmf) in a magnetic circuit is equal to the product of the magnetic flux and the reluctance of the circuit. Mathematically, it can be expressed as:

mmf = flux × reluctance

Let's break down each component of this equation:

1. Magnetomotive Force (mmf):
The magnetomotive force is the force that produces magnetic flux in a magnetic circuit. It is similar to electromotive force in an electrical circuit and is measured in ampere-turns (At). The mmf is directly proportional to the current flowing through a coil and the number of turns in the coil.

2. Magnetic Flux:
Magnetic flux is the measure of the quantity of magnetic field passing through a given area. It represents the number of magnetic field lines passing through a surface and is measured in Weber (Wb). The magnetic flux is directly proportional to the magnetic field strength and the area enclosed by the magnetic circuit.

3. Reluctance:
Reluctance is the resistance offered by a magnetic circuit to the flow of magnetic flux. It is similar to resistance in an electrical circuit and is measured in ampere-turns per Weber (At/Wb). Reluctance depends on the magnetic properties of the materials used in the circuit and the physical dimensions of the circuit. It is inversely proportional to the permeability of the material and the cross-sectional area of the circuit, and directly proportional to the length of the circuit.

In summary, Ohm's law for magnetic circuits states that the mmf required to establish a certain amount of magnetic flux in a magnetic circuit is equal to the product of the flux and the reluctance of the circuit. This law helps in analyzing and calculating the behavior of magnetic circuits, similar to how Ohm's law is used to analyze electrical circuits.