Magnetism — Set 3

Correct Answer: D. F = BIL sinθ

• **F = BIL sinθ** = Force on a current-carrying conductor: F = BIL sinθ, where θ is the angle between current direction and B. • **F = BIL sinθ; maximum when θ = 90°** — At θ = 0° (current parallel to B), force is zero; at 90°, F = BIL. • 💡 Wrong-option analysis: F = B + I + L: simple addition of quantities with different units is meaningless; F = B/I: ratio has wrong units; F = BI/L: divides by L instead of multiplying.

Correct Answer: D. τ = nBIA sinθ

• **τ = nBIA sinθ** = Torque on a current-carrying coil: τ = nBIA sinθ, where θ is the angle between coil plane and field. • **τ_max = nBIA when θ = 90° (coil plane parallel to B)** — This torque drives galvanometers, motors, and meters. • 💡 Wrong-option analysis: τ = nI/B: divides by B instead of multiplying; τ = BI/L: L is length, not area, and n is missing; τ = B/IA: divides by IA instead of multiplying.

Correct Answer: A. Torque is proportional to current for all angles

• **Torque is proportional to current for all angles** = A radial field keeps the angle between coil plane and field always 90°, so τ = nBIA × 1 = nBIA, making deflection ∝ I (linear scale). • **Radial B: sinθ = 1 always → τ = nBIA** — Cylindrical pole pieces create radial field; this gives a uniform scale on the meter. • 💡 Wrong-option analysis: The coil becomes heavier: field shape does not affect coil mass; No magnetic field is needed: a radial field IS a magnetic field; The resistance becomes zero: field geometry has no effect on coil resistance.

Correct Answer: A. Weber

• **Weber** = Magnetic flux Φ = B·A cosθ is measured in weber (Wb); 1 Wb = 1 T·m² = 1 V·s. • **1 Wb = 1 T·m²** — Faraday's law: EMF = −dΦ/dt (volts = webers per second). • 💡 Wrong-option analysis: Tesla: unit of flux density B (= Wb/m²), not flux; Ampere: unit of electric current; Henry: unit of inductance (Wb/A).

Correct Answer: B. 1 T = 1 Wb/m^2

• **1 T = 1 Wb/m²** = Tesla is flux density (flux per unit area), so 1 T = 1 Wb/m². • **B = Φ/A; T = Wb/m²** — Stronger field or same flux through smaller area both increase B in tesla. • 💡 Wrong-option analysis: 1 T = 1 Wb·m²: multiplies instead of divides by area; 1 T = 1 Wb/m: linear not area; 1 T = 1 m²/Wb: inverted, that would be 1/B.

Correct Answer: A. Gauss

• **Gauss** = In CGS, magnetic flux density is measured in gauss (G); 1 T = 10,000 G (or 10⁴ G). • **1 T = 10,000 Gauss** — Earth's field ≈ 0.5 Gauss; refrigerator magnets ≈ 50–200 Gauss. • 💡 Wrong-option analysis: Coulomb: CGS unit of electric charge; Joule: unit of energy; Volt: unit of electric potential.

Correct Answer: D. Oersted

• **Oersted** = In CGS, magnetic field strength H is measured in oersted (Oe); 1 Oe ≈ 79.58 A/m in SI. • **H in CGS: Oersted; H in SI: A/m** — Named after Hans Christian Ørsted who discovered current-magnetism link. • 💡 Wrong-option analysis: Farad: unit of electrical capacitance; Weber: SI unit of magnetic flux; Tesla: SI unit of magnetic flux density.

Correct Answer: A. Very high permeability

• **Very high permeability** = High-permeability materials like mu-metal (μ_r ~ 20,000–100,000) provide easy path for flux, diverting field lines away from the shielded region. • **High μ material guides B lines around protected area** — Used to shield sensitive electronics, MRI rooms, CRT displays. • 💡 Wrong-option analysis: No magnetic response: would provide no preferential path, no shielding; Very low melting point: melting point irrelevant to shielding performance; Very high electrical conductivity only: conductors can provide some AC shielding (eddy currents) but high μ is the primary mechanism for static/DC shielding.

Correct Answer: A. Magnetic field perpendicular to the current

• **Magnetic field perpendicular to the current** = In the Hall effect, the Lorentz force F = qv × B deflects charge carriers sideways, building up a transverse Hall voltage V_H. • **V_H = IB/(nqd); d = thickness** — Hall sensors measure B field strength; also determines sign of charge carriers. • 💡 Wrong-option analysis: Vacuum with no fields: no charges in vacuum to show Hall effect; Uniform gravitational field only: gravity does not cause transverse charge separation; Heated region only: thermal effects cause Seebeck effect, not Hall effect.

Correct Answer: A. Strong magnetic fields and radio waves

• **Strong magnetic fields and radio waves** = MRI aligns hydrogen nuclei (protons) with a strong B field, then uses radiofrequency pulses; the relaxation signal gives tissue images. • **MRI: B₀ ≈ 1.5–3 T; RF pulses at Larmor frequency** — No ionising radiation; excellent soft-tissue contrast. • 💡 Wrong-option analysis: Only gravitational waves: gravitational waves are an astronomical phenomenon, not used medically; Only visible light: visible light cannot penetrate tissue; Only X-rays: X-rays give bone contrast but MRI uses magnetic fields and radio waves.