Ohm's law for a magnetic circuit is given by ratio of: 

Explanation:

Ohm's Law for Magnetic Circuits:

Definition: Ohm's law for a magnetic circuit states that the magnetomotive force (MMF) is equal to the product of the magnetic flux and the magnetic reluctance. This relationship is analogous to Ohm's law in electrical circuits, where the voltage is equal to the product of current and resistance.

Mathematical Representation:

The equation for Ohm's law in a magnetic circuit is:

MMF = Φ × R

• MMF: Magnetomotive force, measured in ampere-turns (At).
• Φ: Magnetic flux, measured in webers (Wb).
• R: Magnetic reluctance, measured in ampere-turns per weber (At/Wb).

Correct Option Analysis:

The correct option is:

Option 3: Magnetomotive force to magnetic reluctance.

This option correctly represents the relationship defined by Ohm's law for magnetic circuits. The magnetomotive force (MMF) is the driving force that creates magnetic flux in a magnetic circuit. When divided by the magnetic reluctance, it gives the magnetic flux, which is analogous to the current in an electrical circuit. Therefore, MMF is proportional to the product of magnetic flux and magnetic reluctance, aligning with the principles of Ohm's law.

Detailed Explanation:

In magnetic circuits, just as in electrical circuits, there is a driving force, a flow, and opposition to flow. These terms correspond to:

• Driving Force: Magnetomotive force (MMF), analogous to voltage in electrical circuits.
• Flow: Magnetic flux (Φ), analogous to current in electrical circuits.
• Opposition: Magnetic reluctance (R), analogous to resistance in electrical circuits.

When MMF is applied across a magnetic circuit, it generates magnetic flux, which flows through the circuit. The opposition to this flow is provided by the magnetic reluctance, which depends on factors like the material's permeability, cross-sectional area, and length of the magnetic path.

The analogy to Ohm's law in electrical circuits makes it easier to understand and analyze magnetic circuits using similar principles. In this context:

• MMF: Represented as the product of current (I) and the number of turns (N) in the coil, i.e., MMF = N × I.
• Magnetic Flux: The quantity of magnetic field passing through a given area, denoted as Φ.
• Magnetic Reluctance: The opposition to the formation of magnetic flux, calculated using the formula R = l/(μ × A), where:
  • l: Length of the magnetic path.
  • μ: Permeability of the material.
  • A: Cross-sectional area of the magnetic path.

Thus, the correct option, "Magnetomotive force to magnetic reluctance," aligns with the established relationship in magnetic circuits.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Magnetic reluctance to magnetic flux.

This option is incorrect because it misrepresents the relationship defined by Ohm's law. Magnetic reluctance is the opposition to magnetic flux, and its ratio to magnetic flux does not define MMF. Instead, MMF is the product of flux and reluctance, as established by the law.

Option 2: Magnetic reluctance to magnetomotive force.

This option is incorrect as well because it inverses the relationship. Magnetic reluctance, when divided by MMF, does not yield a meaningful physical quantity in the context of Ohm's law for magnetic circuits. The flux is obtained by dividing MMF by reluctance, not the other way around.

Option 4: Magnetomotive force to permeance.

This option is partially misleading. Permeance is the reciprocal of reluctance and represents the ease with which magnetic flux can be established in a material. While MMF divided by permeance equals magnetic flux, this option is not the most direct representation of Ohm's law for magnetic circuits, which specifically uses reluctance as the term for opposition.

Conclusion:

Understanding the principles of Ohm's law for magnetic circuits is essential for analyzing magnetic systems. The correct option, "Magnetomotive force to magnetic reluctance," accurately describes the fundamental relationship in such circuits, where MMF drives magnetic flux through a material, overcoming the opposition of magnetic reluctance.