#permeability

Hysteresis, Retentivity, Coercivity and Permanent Magnets

A diamagnetic material has a susceptibility \( \chi = -2 \times 10^{-5} \). What is its magnetic permeability \( \mu \)

**Permanent magnet requirement** is high retentivity to maintain field and high coercivity to resist demagnetization. Ability to retain magnetism after field removal is property of hard ferromagnets, related to domain wall pinning and anisotropy. Magnetic permeability μ = μ₀ (1 + chi) . Given: chi = -2 × 10⁻⁵ . Substitute: μ = μ₀ (1 - 2 × 10⁻⁵) = μ₀ × 0.99998 . Substituting values gives μ₀ × 0.99998, which matches expected magnitude for this magnetic configuration, confirming dipole field dependence on m/r³ and torque relation τ = m B sinθ.

Ref: NCERT > Physics Book > Magnetism and Matter > Hysteresis, Retentivity, Coercivity and Permanent Magnets

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Solenoid with Magnetic Core and Magnetic Properties

A solenoid with magnetic field \( B = 0.8 \, \text{T} \) inside has a core with \( \mu_r = 400 \) and \( n = 800 \, \tex

**Solenoid with magnetic core** produces field B = μ₀ μ_r n I inside, μ₀ = 4π×10⁻⁷ T·m/A, μ_r relative permeability, n = N/L turns per meter, I current. Core enhances field μ_r times, so given B, μ_r, n, current I = B/(μ₀ μ_r n) can be found, illustrating core effect on field strength. B = μ₀ μ_r n I , so I = (B/μ₀ μ_r n) . Given: B = 0.8 T , μ_r = 400 , n = 800 m⁻¹ , μ₀ = 4π × 10⁻⁷ . Substitute: I = (0.8/4π × 10⁻⁷ × 400 × 800) = (0.8/4π × 3.2 × 10⁻²) ≈

Ref: NCERT > Physics Book > Magnetism and Matter > Solenoid with Magnetic Core and Magnetic Properties

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Solenoid with Magnetic Core and Magnetic Properties

A solenoid produces \( B = 0.96 \, \text{T} \) with a core of \( \mu_r = 300 \) and \( n = 1000 \, \text{m}^{-1} \). Wha

**Solenoid with magnetic core** produces field B = μ₀ μ_r n I inside, μ₀ = 4π×10⁻⁷ T·m/A, μ_r relative permeability, n = N/L turns per meter, I current. Core enhances field μ_r times, so given B, μ_r, n, current I = B/(μ₀ μ_r n) can be found, illustrating core effect on field strength. B = μ₀ μ_r n I , so I = (B/μ₀ μ_r n) . Given: B = 0.96 T , μ_r = 300 , n = 1000 m⁻¹ , μ₀ = 4π × 10⁻⁷ . I = (0.96/4π × 10⁻⁷ × 300 × 1000) = (0.96/3.769 × 10⁻¹) ≈ 2.548 A ≈

Ref: NCERT > Physics Book > Magnetism and Matter > Solenoid with Magnetic Core and Magnetic Properties

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Solenoid with Magnetic Core and Magnetic Properties

A solenoid produces \( B = 0.6 \, \text{T} \) with a core of \( \mu_r = 200 \) and \( n = 1000 \, \text{m}^{-1} \). What

**Magnetic field inside solenoid** with core B = μ₀ μ_r n I is uniform, direction along axis given by right-hand grip rule. For n = 2000 m⁻¹, μ_r = 400, B = 1.2 T, I = 1.2/(4π×10⁻⁷×400×2000) ≈ 1.19 A, showing modest current produces tesla-level field with high μ_r core. B = μ₀ μ_r n I , so I = (B/μ₀ μ_r n) . Given: B = 0.6 T , μ_r = 200 , n = 1000 m⁻¹ , μ₀ = 4π × 10⁻⁷ . I = (0.6/4π × 10⁻⁷ × 200 × 1000) = (0.6/2.513 × 10⁻¹) ≈ 2.39 A ≈ 2.4 A .

Ref: NCERT > Physics Book > Magnetism and Matter > Solenoid with Magnetic Core and Magnetic Properties

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Membrane Transportation

What is the correct order of permeability through the lipid bilayer?

Permeability across pure phospholipid bilayer without proteins follows solubility-diffusion model where permeability coefficient P equals oil-water partition K times diffusion within hydrocarbon D divided by thickness delta. Consequently small hydrophobic molecules lacking hydrogen bonds partition efficiently into acyl core exhibiting highest permeability. Gases O2 and CO2 permeability around ten to fifty cm per second diffusing almost freely enabling instantaneous alveolar capillary equilibration and mitochondrial respiration. Water despite small size eighteen Daltons polar forming bonds permeability three orders lower around 0.001 cm/s still appreciable and augmented hundredfold by aquaporins for kidney reabsorption. Glucose larger one eighty Daltons five hydroxyls poorly partitions permeability about 10^-6 cm/s six orders less than water needing GLUT carriers for physiological uptake. Small monovalent ions Na+ K+ Cl- face enormous Born self-energy around three hundred kilojoules plus electrostatic cost in low dielectric about two permeability below 10^-12 negligible without selective channels. Large polyanions ATP four negative charges and RNA polyphosphate backbone essentially impermeant below 10^-14 relying entirely on specific transporters. This hierarchy explains dependence on selective transport proteins for polar metabolites while gases exchange without assistance.

Ref: Alberts et al., Molecular Biology of the Cell, 6th ed., Chapter 11: Relative Permeability – O2, CO2, H2O, Glucose, Ions, RNA.

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Microbial Physiology

The permeability of the Gram-negative outer membrane is controlled by:

Gram-negative outer membrane serves as molecular sieve preventing entry of large hydrophilic and hydrophobic antibiotics like vancomycin, daptomycin, and bile salts. Permeability is governed primarily by porins, abundant trimeric beta-barrel proteins forming water-filled diffusion channels with constrictions determined by internal loop L3. General porins OmpF and OmpC allow passive diffusion of molecules below about 600 daltons, including nutrients and some beta-lactams, dependent on charge and size. Specific porins like LamB and ScrY facilitate uptake of maltodextrins and sucrose via binding site within channel, increasing efficiency. Regulation of porin abundance through two-component system EnvZ-OmpR and small RNAs like MicF enables adaptation to osmolarity, pH, and antibiotic pressure, with porin loss conferring resistance to carbapenems. Lipoteichoic acids are Gram-positive polymers, peptidoglycan thickness controls lysozyme sensitivity in Gram-positives, and ether bonds characterize archaeal lipids not controlling Gram-negative permeability. Hence porins act as major determinants of outer membrane exclusion limit, linking envelope permeability to nutrient acquisition and intrinsic drug resistance mechanisms studied by Nikaido pioneering work.

Ref: Nikaido, Microbiol Mol Biol Rev 2003, Outer Membrane Porins and Resistance; Delcour, BBA 2009, Porin Regulation.

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