(i) As the magnetic field strength (H) increases, reluctance? (ii) As the magnetic flux density (B) increases,

Question

(i) As the magnetic field strength (H) increases, reluctance? (ii) As the magnetic flux density (B) increases, reluctance?

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Option A: (i) Increase (ii) Decrease

Explanation & Concepts:
Reluctance ($ mathcal{R}$) is the opposition offered by a magnetic circuit to the creation of magnetic flux. For non-linear ferromagnetic materials operating in the saturation region, an increase in magnetic field strength ($H$) causes permeability ($ mu$) to decrease due to magnetic saturation. Consequently, as $H$ increases, reluctance increases, whereas as magnetic flux density ($B$) increases (in the initial/linear region prior to extreme saturation), reluctance decreases.

Working Principle: In ferromagnetic materials, the magnetic permeability $ mu$ is non-constant and defined by the slope or ratio $B/H$ on the B-H magnetization curve. In the initial magnetization region, as flux density $B$ increases, the material becomes more magnetized and permeable, leading to a decrease in reluctance. However, beyond the knee point, as magnetic field strength $H$ increases continuously into the saturation region, the differential permeability drops drastically, causing the reluctance of the magnetic path to increase significantly.

Key Formulas: $\mathcal{R} = \frac{l}{\mu A} = \frac{l}{\mu_0 \mu_r A}$ — Reluctance in terms of magnetic circuit parameters; $B = \mu H \implies \mu = \frac{B}{H}$ — Relation between magnetic flux density $B$, field strength $H$, and permeability $\mu$; $\mathcal{R} = \frac{\mathcal{F}}{\Phi} = \frac{N I}{\Phi}$ — Hopkinson's law for magnetic circuits

Key Points: Reluctance is inversely proportional to magnetic permeability ($ mu$).; In ferromagnetic materials, as magnetic field strength $H$ drives the core into deep saturation, the permeability $ mu$ decreases, causing reluctance to increase.; As flux density $B$ increases in the operating linear region, permeability $ mu$ effectively increases, causing reluctance to decrease.

Applications: Design of magnetic circuits in transformers and electric machines to minimize reluctance and magnetizing current.; Analysis of magnetic saturation in electrical steel cores.

Additional Info: Option A correctly identifies that reluctance increases with an increase in magnetic field strength $H$ (due to saturation reducing $ mu$) and decreases with an increase in magnetic flux density $B$ prior to saturation.. Options B, C, and D fail to correctly account for the inverse relationship between reluctance and permeability $ mu = B/H$ under varying $B$ and $H$ conditions.

Answer: A is correct — As magnetic field strength $H$ increases into saturation, permeability $\mu$ drops, causing reluctance to increase; whereas increasing magnetic flux density $B$ increases $\mu$, causing reluctance to decrease.

Exam Tip: Always relate magnetic reluctance ($ mathcal{R}$) to electrical resistance ($R$). Since $ mathcal{R} = \frac{l}{\mu A}$, any parameter that decreases permeability $ mu$ (like high $H$ causing magnetic saturation) will directly increase reluctance.

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Option B: (i) Increase (ii) Increase

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Option C: (i) Decrease (ii) Increase

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Option D: (i) Constant (ii) Constant

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