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Magnetic fields and alternating currents (A Level)

20. Magnetic Fields — Cambridge AS & A Level Physics 9702 Revision Notes & Topical Questions

10 min read 10 parts Lesson 23 of 24 Unit quiz

📚 Cambridge AS & A Level Physics 9702 Hub / Topical Revision
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20. Magnetic Fields — Cambridge AS & A Level Physics 9702 — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Describe magnetic fields and the forces they exert on currents and moving charges, explain the Hall effect and velocity selectors, and apply Faraday's and Lenz'…

  • Magnetic field (B-field)
  • Detecting fields
  • Field lines
  • Earth's field
  • Magnetic flux density B
  • Force on a conductor

Section 1 of 10Magnetic fields and field lines

  • Magnetic field (B-field) = a field of force created by moving electric charges or permanent magnets; a stationary charge produces no magnetic field.
  • Detecting fields
    • they pull on magnetic materials such as iron and deflect a plotting compass, and iron filings map the pattern.
  • Field lines
    • arrows leave a north pole and enter a south pole, showing the direction of the force on a free north pole.
    • Lines closer together mean a stronger field, strongest at the poles, and lines never cross.
    • Like poles repel and unlike poles attract.
    • A uniform field has equally spaced parallel lines, for example between two opposite poles held close.
  • Earth's field
    • it acts like a bar magnet, and a compass needle points to geographic north because that is near the Earth's magnetic south pole.

Section 2 of 10Flux density and force on a current-carrying conductor

  • Magnetic flux density B = the force exerted per unit current per unit length on a straight conductor perpendicular to the field.
    • The unit is the tesla (T): 1 T gives a force of 1 N on a 1 m wire carrying 1 A at right angles to the field.
    • The flux density is higher where the field lines are closer together.
    • The Earth's field is about 0.032 mT and a fridge magnet about 5 mT.
  • Force on a conductor
    • F = BIL sin θ, where θ is the angle between the conductor and the field and L the length in the field.
    • The maximum force is F = BIL when the conductor is perpendicular to the field (θ = 90°), with F, B and I mutually perpendicular.
    • The force is zero when the conductor is parallel to the field (θ = 0°).
    • The force increases with larger B, I or length in the field.
  • Conventional current
    • it runs from positive to negative, opposite to electron flow.

Section 3 of 10Fleming's left-hand rule

  • Hand
    • hold the thumb, first finger and second finger of the left hand at right angles to each other.
  • First finger
    • the direction of the magnetic Field B.
  • Second finger
    • the direction of conventional Current I.
      • (flow of positive charge)
  • Thumb
    • the direction of Motion, the force F on the conductor.
  • Page symbols
    • a dot (⊙) means a field out of the page, like the tip of an arrow approaching, and a cross (⊗) means into the page, like the feathers receding.
  • Generators
    • the right-hand rule is for generators and is different.

Section 4 of 10Force on a moving charge and circular motion

  • Equation
    • F = BQv sin θ, with θ the angle between the velocity and the field.
    • The maximum force is BQv when the particle moves perpendicular to the field.
    • There is no force when it moves parallel to the field.
  • Direction
    • use Fleming's left-hand rule with the second finger along the direction of conventional current.
    • For a positive charge that is the direction of motion, and for a negative charge (electrons) it is opposite to the motion.
  • Distinction
    • BQv is for an isolated moving charge and BIL is for a current in a wire.
  • Why a circle
    • the force is perpendicular to the velocity, so it changes direction but not speed, and acts as the centripetal force.
  • Radius
    • equating BQv with mv2/r gives r = mv/(BQ).
ChangeEffect on radius r
Larger speed vLarger circle (r ∝ v)
Larger mass mLarger circle (r ∝ m)
Larger charge QSmaller circle (r ∝ 1/Q)
Stronger field BSmaller circle (r ∝ 1/B)
  • Acceleration
    • the magnetic force causes the centripetal acceleration a = F/m.

Section 5 of 10The Hall effect

  • Hall effect
    • when a field is applied perpendicular to the current in a conductor, the moving charge carriers are pushed to one side,
    • so one side becomes negative and the other positive.
  • Hall voltage VH = the p.d. across the conductor produced by the perpendicular field, VH = BI/(ntq).
    • n is the number density of carriers (m−3), t the thickness and q the charge of each carrier.
    • A smaller n gives a larger VH, so semiconductors are used for Hall probes.
    • With positive carriers in place of electrons (same current direction), the Hall voltage reverses.
  • Derivation
    • the two sides act as oppositely charged plates with E = VH/d.
    • In equilibrium the electric and magnetic forces on a carrier are equal and opposite, qE = Bqv, so VH/d = Bv.
    • With I = nAvq and A = dt, v = I/(nAq) gives VH = BI/(ntq).
  • Hall probe
    • a thin slice with a flat end, connected to a voltmeter, used to measure flux density.
    • It is held with the field perpendicular to the flat surface for a maximum reading.
    • Tilting reduces the reading, which is zero when the field is parallel to the surface.
    • VH is directly proportional to B, so after calibration it measures B, even the Earth's field.

Section 6 of 10Velocity selector

  • Velocity selector = perpendicular electric and magnetic fields in a vacuum, between oppositely charged plates, that pass only charged particles of one speed undeflected; it is used in mass spectrometers.
  • Balance
    • the electric force EQ and magnetic force BQv are equal and opposite at the chosen speed, so EQ = BQv.
  • Selected speed
    • v = E/B, independent of the charge.
  • Other speeds
    • faster or slower particles are deflected by the unbalanced force and hit a plate.
  • Gravity
    • it is negligible compared with the electric and magnetic forces.

Section 7 of 10Fields due to currents

  • Straight wire
    • concentric circular field lines centred on the wire, closer near the wire where the field is strongest.
    • Reversing the current reverses the field.
    • Right-hand grip rule: thumb along the conventional current, curled fingers give the field direction.
  • Solenoid
    • a long coil gives a field like a bar magnet, with lines leaving the north pole and re-entering at the south pole.
    • For a coil, the curled fingers follow the current and the thumb gives the field inside, towards the north pole.
    • The end where the current appears anticlockwise is the north pole.
  • Strengthening
    • add more turns and a soft iron core, which can increase the field several hundred times.
  • Parallel currents
    • each wire is in the field of the other, so each feels a force.
    • Currents in the same direction attract and in opposite directions repel.
    • The two forces are equal and opposite, as Newton's third law requires.

Section 8 of 10Magnetic flux and flux linkage

  • Magnetic flux Φ = the product of flux density and the area perpendicular to the field, Φ = BA, in webers (Wb).
    What the symbols mean: Φ = magnetic flux (Wb) · B = magnetic flux density (T) · A = area at right angles to the field (m2)
  • Angled area
    • Φ = BA cos θ, where θ is the angle between the field lines and the normal to the area.
    • The flux is maximum (BA) when the field is perpendicular to the plane (θ = 0°) and zero when it is parallel (θ = 90°).
  • Flux linkage = the flux multiplied by the number of turns, NΦ = BAN cos θ, in Wb turns.
  • Changing flux
    • an e.m.f. is induced when B, A or the angle changes with time.

Section 9 of 10Electromagnetic induction

1Induction2 points
  • an e.m.f. is induced when a conductor cuts magnetic field lines or the field around it changes.
  • Work is done on the charges in the conductor, separating them.
2Magnet and coil4 points
  • a stationary magnet gives a zero reading.
  • Pushing the magnet in gives a reading and pulling it out gives the opposite sign.
  • Faster movement, more turns and a stronger magnet give a larger e.m.f.
  • The e.m.f. exists only while the magnet moves, because only then does the flux change.
3Wire between magnets2 points
  • moving a wire across the field induces an e.m.f., opposite on the return.
  • It is larger with a longer wire, faster movement and stronger magnets.

Section 10 of 10Faraday's and Lenz's laws

  • Faraday's law = the magnitude of the induced e.m.f. is directly proportional to the rate of change of flux linkage, ε = NΔΦ/Δt.
    What the symbols mean: ε = induced e.m.f. (V) · N = number of turns · ΔΦ = change of flux (Wb) · Δt = time taken (s); the minus sign is Lenz’s law
  • Lenz's law = the induced e.m.f. acts in a direction that opposes the change causing it, so ε = −NΔΦ/Δt.
  • Verifying Lenz's law
    • push a known pole of a bar magnet into a coil connected to a sensitive ammeter, with no cell.
    • The ammeter shows a current, and the induced field repels the approaching magnet.
    • Reversing the magnet reverses the deflection.
    • Use the right-hand grip rule on the solenoid, with fingers along the current and thumb along the induced field.
  • Alternating supply
    • with an a.c. supply the induced e.m.f. alternates at the same frequency.

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