Magnetism — Set 5

Correct Answer: B. μ/μ0

• **μ/μ₀** = Relative permeability μ_r = μ/μ₀; it is the ratio of a material's permeability to that of vacuum. • **μ_r = μ/μ₀; dimensionless** — For iron μ_r ~ 5000; for vacuum μ_r = 1; diamagnets μ_r slightly < 1. • 💡 Wrong-option analysis: μ − μ₀: difference, has units, not dimensionless; μ + μ₀: sum does not define relative permeability; μ₀/μ: inverted ratio, would be 1/μ_r.

Correct Answer: B. χ = M/H

• **χ = M/H** = Susceptibility χ = M/H, where M is magnetization (magnetic moment per unit volume) and H is field strength. • **χ = M/H; dimensionless; χ > 0 paramagnetic; χ < 0 diamagnetic** — Large positive χ (>> 1) means ferromagnetic. • 💡 Wrong-option analysis: χ = H/M: inverted definition, that would be 1/χ; χ = μ₀/μ: that involves permeability values, not the standard susceptibility definition; χ = B/Φ: B/Φ = 1/A (per area), not susceptibility.

Correct Answer: A. B = μ0 H

• **B = μ₀H** = In vacuum, B = μ₀H, where μ₀ = 4π × 10⁻⁷ T·m/A is the vacuum permeability. • **B = μ₀H (vacuum); B = μ₀μ_r H (material)** — H describes the driving field; B includes the material response. • 💡 Wrong-option analysis: B = H/μ₀: inverted μ₀, gives wrong units and magnitude; B = μ₀/H: product divided by H is dimensionally wrong; B = H + μ₀: adding quantities with different units is nonsensical.

Correct Answer: C. 4π × 10^-7 T·m/A

• **4π × 10⁻⁷ T·m/A** = Vacuum permeability μ₀ = 4π × 10⁻⁷ T·m/A ≈ 1.2566 × 10⁻⁶ T·m/A. • **μ₀ = 4π × 10⁻⁷ T·m/A** — Appears in Ampere's law and Biot-Savart law; links current to magnetic field. • 💡 Wrong-option analysis: 9.8: acceleration due to gravity (g in m/s²); 6.67 × 10⁻¹¹: gravitational constant G (N·m²/kg²); 3 × 10⁸: speed of light c (m/s) — note: c = 1/√(μ₀ε₀).

Correct Answer: C. B = μ0 n I

• **B = μ₀nI** = Inside a long solenoid, B = μ₀nI where n is the number of turns per unit length and I is current. • **B = μ₀nI; uniform inside long solenoid** — Doubling current or doubling turns per unit length both double B. • 💡 Wrong-option analysis: B = n/μ₀: divides instead of multiplies; gives wrong units; B = μ₀/I: divides by I instead of multiplying; B = I/R: Ohm's law for current, not a field formula.

Correct Answer: D. Increase the current through the coil

• **Increase the current through the coil** = B = μ₀nI inside solenoid; increasing I directly increases B and magnetizes the core more strongly. • **B ∝ I (for fixed n); increasing I → stronger electromagnet** — Also increasing n (turns per length) or inserting iron core increases B. • 💡 Wrong-option analysis: Decrease the number of turns in the coil: fewer turns means weaker field; Use a non-conducting thread instead of wire: no current → no magnetic field; Remove the coil completely: eliminates the source of field entirely.

Correct Answer: A. Retain magnetization after the field is removed

• **Retain magnetization after the field is removed** = Retentivity (remanence) is the value of B (or M) remaining in the material when the magnetizing field H is returned to zero. • **High retentivity → permanent magnet; low retentivity → soft magnet** — Steel: high retentivity; soft iron: low retentivity. • 💡 Wrong-option analysis: Change color in a magnetic field: not a standard magnetic property; Conduct electric current: that is electrical conductivity, unrelated to retentivity; Stop all magnetic fields permanently: that describes an idealized magnetic shield, not retentivity.

Correct Answer: A. Reduce magnetization to zero

• **Reduce magnetization to zero** = Coercivity (coercive force) is the reverse H field required to bring B (or M) back to zero after the material was magnetized. • **High coercivity → hard to demagnetize → good permanent magnet** — Alnico: high coercivity; soft iron: very low coercivity. • 💡 Wrong-option analysis: Increase magnetization quickly: that relates to initial susceptibility, not coercivity; Make the material conduct better: electrical conductivity is unrelated to coercivity; Create electric charges: magnetization does not create free electric charges.

Correct Answer: B. Energy loss per cycle per unit volume

• **Energy loss per cycle per unit volume** = The area enclosed by the B-H hysteresis loop equals energy dissipated as heat per unit volume per complete magnetization cycle. • **Loop area (J/m³) → heat per cycle per volume** — Minimizing this loss is crucial for transformer and motor cores. • 💡 Wrong-option analysis: The speed of sound in the material: acoustics is unrelated to B-H loops; Only the temperature change: temperature is the effect of energy loss, not what the area directly represents; Only the mass of the material: mass is not encoded in the B-H loop shape.

Correct Answer: B. 1/absolute temperature

• **1/absolute temperature** = Curie law: χ = C/T, where C is the Curie constant and T is absolute temperature in kelvin. • **χ ∝ 1/T (Curie law)** — Higher T increases thermal agitation, disrupts alignment of atomic moments, and reduces susceptibility. • 💡 Wrong-option analysis: Area of the coil: coil area is irrelevant to bulk susceptibility of paramagnets; Square of the current: Curie law relates to temperature, not current; Absolute temperature: χ is inversely (not directly) proportional to T.