If the length of the magnetic path is increased while keeping the cross-sectional area and the magnetomotive force (MMF) constant, which of the following will occur?

Explanation:

Magnetic Flux and Reluctance

Definition: Magnetic flux (Φ) is a measure of the total magnetic field passing through a given area. It is expressed in Weber (Wb). Reluctance (ℜ), on the other hand, is the opposition offered by a magnetic circuit to the flow of magnetic flux, analogous to resistance in an electrical circuit. Reluctance is given by the formula:

ℜ = l / (μ × A)

Where:

• l = Length of the magnetic path (in meters)
• μ = Permeability of the material (in Henry/meter)
• A = Cross-sectional area of the magnetic path (in square meters)

The relationship between the magnetomotive force (MMF), reluctance, and magnetic flux is given by:

Φ = MMF / ℜ

Where:

• Φ = Magnetic flux (in Weber)
• MMF = Magnetomotive force (in Ampere-turns)
• ℜ = Reluctance (in Ampere-turns per Weber)

Correct Option Analysis:

The correct option is:

Option 4: The flux will decrease.

If the length of the magnetic path is increased while keeping the cross-sectional area (A) and magnetomotive force (MMF) constant, the reluctance of the magnetic circuit will increase. This is because reluctance (ℜ) is directly proportional to the length of the magnetic path (l). As reluctance increases, the magnetic flux (Φ), which is inversely proportional to reluctance, will decrease. This can be mathematically expressed as:

Φ = MMF / ℜ

With a higher reluctance (ℜ) due to an increased length (l) of the magnetic path, the denominator in the above equation becomes larger, resulting in a smaller value of Φ. Thus, the magnetic flux will decrease