⚠ Borderline Questions & Answers
These appeared in GE-2/GE-4 exams but are NOT listed verbatim in the PHYS7021 syllabus text. Keep them as backup (examiners sometimes repeat them); confirm with your lecturer.
GE-2 side
Given: 2a = 3 cm = 0.03 m, q = 5 μC, E = 2×104 N/C. Formula: τ = pE sinθ, p = q·2a.
- p = 5×10−6 × 0.03 = 1.5×10−7 C·m.
- τmax (θ = 90°) = pE = 1.5×10−7 × 2×104 = 3×10−3 N·m.
- τmin (θ = 0°) = 0.
∴ τ_max = 3×10⁻³ N·m ; τ_min = 0
- Forces +qE and −qE are equal and opposite ⇒ no net force (dipole does not translate).
- They form a couple ⇒ torque τ = pE sinθ, which rotates the dipole.
- It turns until p aligns with E (stable equilibrium, U = −pE).
∴ Torque pE sinθ aligns the dipole; no translation
Given: q = 1 μC, 2a = 0.02 m ⇒ p = 2×10−8 C·m; E = 2.5×104 N/C; θ = 30°.
- τ = pE sin30° = 2×10−8 × 2.5×104 × 0.5.
- = 2.5×10−4 N·m.
∴ τ = 2.5×10⁻⁴ N·m
Formula: F = q(E + v×B).
- v×B = (3î+2ĵ)×(ĵ+2k̂) = 3(î×ĵ) + 6(î×k̂) + 2(ĵ×ĵ) + 4(ĵ×k̂) = 3k̂ − 6ĵ + 0 + 4î = 4î − 6ĵ + 3k̂.
- E + v×B = (6+4)î + (6−6)ĵ + (3+3)k̂ = 10î + 6k̂.
- F = 1.6×10−19 × √(102+62) = 1.6×10−19 × √136 ≈ 1.87×10−18 N, along (10î+6k̂)/√136.
∴ F ≈ 1.87×10⁻¹⁸ N along (10î+6k̂)/√136
- Magnetic force F = qv×B is always perpendicular to velocity.
- Power = F·v = 0 at every instant.
- Hence work = 0; the field changes the direction of velocity, never the speed.
∴ Work = 0
Given: L = 0.1 m, d = 0.02 m, I1 = 20 A, I2 = 30 A. Formula: F = (μ0/2π)(I1I2/d)L.
- F = (2×10−7) × (20×30/0.02) × 0.1 = (2×10−7) × (3×104) × 0.1.
- = 6×10−4 N (attractive if currents are in the same direction).
∴ F = 6×10⁻⁴ N
Given: A = 0.25 m2, d = 0.01 m, V = 10 V.
- E = V/d = 10/0.01 = 1000 V/m.
- F = ½ε0E2A = 0.5 × 8.85×10−12 × 106 × 0.25.
- ≈ 1.1×10−6 N.
∴ F ≈ 1.1×10⁻⁶ N
GE-4 side
Formula: V = (Imax − Imin)/(Imax + Imin); intensity ∝ (amplitude)2.
- Imax ∝ (2+1)2 = 9; Imin ∝ (2−1)2 = 1.
- V = (9−1)/(9+1) = 8/10 = 0.8.
∴ V = 0.8
- Definition: resolving power = λ/dλ — the ability to separate two close wavelengths.
- Grating: by Rayleigh's criterion the principal maximum of one wavelength must fall on the first minimum of the other ⇒ R = nN (order × total illuminated rulings).
- Optical instrument: e.g., telescope R = D/1.22λ (D = aperture); microscope R = 2μ sinθ/1.22λ.
∴ R = λ/dλ ; grating R = nN
- The property of certain substances (sugar solution, quartz, camphor, turpentine) to rotate the plane of polarization of light passing through them.
- Measured with a polarimeter; specific rotation θ = α/(l·c) (α = observed rotation, l = path length, c = concentration).
∴ Rotation of polarization plane; e.g. sugar solutions