Magnetic Fields and Electromagnetism

Jun 8, 2025

Overview

This lecture covers all AQA A-level Physics content on magnetic fields and electromagnetism, focusing on forces, induction, key formulas, and applications like motors, particle motion, transformers, and AC.

Force on Current-Carrying Wires

  • A current-carrying wire in a magnetic field experiences a force: ( F = BIL\sin\theta ), where θ is the angle between field and wire.
  • Maximum force when wire is perpendicular to field (( \theta = 90^\circ )), zero force when parallel (( \theta = 0^\circ, 180^\circ )).
  • Direction of force found using Fleming’s left-hand rule (thumb: force, first finger: field, second finger: current).

Electric Motors Example

  • Force on sides of a square coil: ( F = BIL ); zero force for wire parallel to field.
  • Net moment about rotation axis: moment = sum of forces × distance to pivot, ( \text{net moment} = 4 \times 10^{-3}L^2 ).
  • In equilibrium, magnetic force balances weight: ( BIL = mg \Rightarrow I = mg/BL ).

Magnetic Flux Density and SI Units

  • Magnetic flux density (B) measured in Tesla (T); calculated as ( B = F/(IL) ).
  • 1 T = 1 N A(^{-1}) m(^{-1}); SI base units: kg A(^{-1}) s(^{-2}).

Force on Moving Charges

  • Force on charge: ( F = Bqv ) (velocity perpendicular to field), or ( F = Bqv\sin\theta ).
  • Magnetic force acts as centripetal force for charged particles: ( Bqv = mv^2/r \Rightarrow r = mv/(Bq) ).
  • Path is circular in magnetic field; in electric field, path is a parabola.

Magnetic Flux and Linkage

  • Magnetic flux ( \phi = BA\cos\theta ), with θ as angle between field and normal to area.
  • Flux linkage for N turns: ( N\phi = NBA\cos\theta ).
  • Unit of magnetic flux and linkage: Weber (Wb).

Electromagnetic Induction (Faraday’s and Lenz's Law)

  • Induced emf: ( \text{emf} = \Delta(N\phi)/\Delta t ); greater rate of flux change induces higher emf.
  • Lenz’s law: induced emf opposes the change causing it.
  • Example: emf in a moving conductor ( \text{emf} = BLv ), where v = velocity perpendicular to field.
  • Emf in rotating coil: peak emf ( = BAN\omega ), where ( \omega = 2\pi f ).

Alternating Current (AC) and RMS Values

  • AC alternates direction; voltage-time graph is sinusoidal.
  • RMS voltage ( V_{\text{rms}} = V_{\text{peak}}/\sqrt{2} ); peak-to-peak voltage ( = 2V_{\text{peak}} ).
  • Average AC power: ( P_{\text{avg}} = I_{\text{rms}}V_{\text{rms}} ).

Transformers

  • Transformer equation: ( V_s/V_p = N_s/N_p ) and ( V_pI_p = V_sI_s ) (ideal transformer).
  • Efficiency ( = \text{Power out}\text{secondary} / \text{Power in}\text{primary} ).
  • Eddy currents cause energy loss; core is laminated to reduce them.

Key Terms & Definitions

  • Magnetic Flux Density (B) — force per unit current per unit length on a perpendicular conductor in a magnetic field.
  • Tesla (T) — SI unit of magnetic flux density.
  • Magnetic Flux (( \phi )) — product of perpendicular magnetic flux density and area (( BA\cos\theta )).
  • Flux Linkage — total flux through N coils (( N\phi )).
  • Faraday’s Law — emf is proportional to the rate of change of flux linkage.
  • Lenz’s Law — induced emf opposes the change producing it.
  • Root Mean Square (RMS) — effective value of alternating current or voltage.
  • Eddy Currents — currents induced in transformer cores, causing losses.

Action Items / Next Steps

  • Practice applying Fleming’s left-hand rule and AC/transformer formulas to problems.
  • Review required practicals linked to electromagnetic induction.
  • Memorize key definitions and derivations for exam questions.

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