ZIMSEC A Level · Physics · Form 6
Magnetic forces
- Force on a current-carrying conductor: F = BIL sin θ (Fleming's left-hand rule).
- Force on a moving charge: F = Bqv sin θ; in a uniform field a charged particle moves in a circle of radius r = mv/(Bq).
Worked example: An electron (m = 9.11 × 10⁻³¹ kg) moves at 2.0 × 10⁷ m s⁻¹ perpendicular to a field of 5.0 × 10⁻³ T. Find the radius of its path.
r = mv/(Bq) = (9.11 × 10⁻³¹ × 2.0 × 10⁷) ÷ (5.0 × 10⁻³ × 1.6 × 10⁻¹⁹) = 0.0228 m ≈ 2.3 cm
- Hall effect: a voltage across a conductor in a magnetic field; used in Hall probes to measure B.
Electromagnetic induction
- Magnetic flux Φ = BA cos θ; flux linkage = NΦ.
- Faraday's law: induced e.m.f. = rate of change of flux linkage, E = −N dΦ/dt.
- Lenz's law: the induced current opposes the change that produces it (conservation of energy).
Worked example: A 200-turn coil of area 0.010 m² is in a field that falls from 0.50 T to 0 in 0.10 s. Find the average induced e.m.f.
E = NΔΦ/Δt = 200 × (0.50 × 0.010) ÷ 0.10 = 10 V
Alternating current
- Root-mean-square values: Vrms = V₀/√2, Irms = I₀/√2; mean power = Irms Vrms.
- Transformers: Vs/Vp = Ns/Np; high-voltage transmission reduces I²R losses.
- Rectification using diodes (half-wave and full-wave bridge) with a smoothing capacitor.
Exam tip: Lenz's law is about direction – always state what change the induced current opposes.
Check yourself
- Find the force on a 0.20 m wire carrying 3.0 A at right angles to a 0.40 T field.
- The peak voltage of a supply is 325 V. Find the r.m.s. voltage.
- State Lenz's law.
Show answers
- 0.24 N
- 325 ÷ √2 ≈ 230 V
- The direction of an induced e.m.f. or current is such that it opposes the change producing it.
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