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Theme D — Fields

D.3.1 Magnetic Force on a Current-Carrying Conductor — IB Physics HL Revision Notes & Topical Questions

5 min read 11 parts Lesson 28 of 39 1 quiz

📚 IB Physics HL Hub / Topical Revision
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pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

D.3.1 Magnetic Force on a Current-Carrying Conductor — IB PHYSICS SL notes: Calculate the size and direction of the force on a straight wire carrying current in a uniform magnetic field.Moving charges — a magnetic field exerts a force on every moving charge, and a current is a st…

  • Whole wire
  • Observation
  • Applications
  • Magnetic flux density (B)
  • What the symbols mean
  • Increasing the force

Part 1 of 9Why a current feels a force

Moving charges
  • Moving charges a magnetic field exerts a force on every moving charge, and a current is a stream of moving charges
Whole wire
  • Whole wire the force acts on the charge carriers, but they are locked in the lattice, so the wire is pushed sideways
Own field
  • Own field a current-carrying conductor produces its own field, which interacts with the external field
Observation
  • Observation a copper rod in a circuit placed in a uniform field accelerates in the direction of the force when current flows
Applications
  • Applications electric motors, loudspeakers and moving-coil meters

Part 2 of 9Magnetic flux density

1Magnetic flux density (B)
  • Magnetic flux density (B) the strength of the field, measured in tesla (T)
2Tesla
  • Tesla the field that produces a force of 1 N on a 1 m length of wire carrying 1 A at right angles to the field
  • 1 T = 1 N A−1 m−1.

Part 3 of 9The equation

The equation
Equation
  • F = BIL sin θ
    What the symbols mean: F = force on the wire (N) · B = magnetic flux density (T) · I = current (A) · L = length of wire in the field (m) · θ = angle between wire and field
Symbols
  • F is the force on the wire in N.
  • B is the magnetic flux density in T.
  • I is the conventional current in A.
  • L is the length of wire inside the field in m.
  • θ is the angle between the current direction and the field.
Increasing the force
  • Increasing the force raise the field strength, the current or the length in the field
Perpendicular wire
  • Perpendicular wire at θ = 90° the force is maximum, F = BIL
Parallel wire
  • Parallel wire at θ = 0° sin θ = 0, so there is no force
Component
  • Component only the component of the field perpendicular to the wire, B sin θ, produces force

Part 4 of 9Finding the direction

Mutually perpendicular
  • Mutually perpendicular the force, the field and the current are perpendicular to each other
Fleming's left-hand rule
  • Fleming's left-hand rule thumb along the force, first finger along the field and second finger along the conventional current
Right-hand version
  • Right-hand version fingers along the field, thumb along the conventional current and the force comes out of the palm
Check
  • Check always test the rule you use on a case you know
Conventional current
  • Conventional current it flows from positive to negative, opposite to electron flow
Reversal
  • Reversal reversing either the current or the field reverses the force

Part 5 of 9Diagram symbols

Field out of the page
  • Field out of the page dots, like the tip of an arrow coming towards you
Field into the page
  • Field into the page crosses, like the feathers of an arrow moving away
Example
  • Example a current to the right in a field into the page gives a vertical force, up or down depending on the rule

Part 6 of 9Where the formula comes from

1
Take a length L of wire with n carriers per unit volume, area A, charge q and drift speed v.
2
The current is I = nAvq.
3
The number of carriers in the section is nAL.
4
Each feels a force qvB for perpendicular motion.
5
The total is F = nAL × qvB = (nAvq) × LB = BIL.
  • Meaning
    • the wire force is the force on a single moving charge added up for all the charges

Part 7 of 9Applications

DC motor
  • DC motor a coil in a field has current in opposite directions on opposite sides, so the forces form a couple that turns it
  • A commutator reverses the current each half turn to keep the turning in one direction.
Loudspeaker
  • Loudspeaker a coil attached to a cone moves back and forth with the varying signal current

Part 8 of 9Current balance

1
Hang a wire loop from a balance in the field.
2
Pass a current through the wire.
3
Record the change in apparent mass Δm.
4
Use F = Δm g = BIL, so B = Δm g / IL.
Graph
  • F against I is a straight line through the origin with gradient BL
Angle graph
  • Angle graph force against angle is a sine curve from 0° to 180°

Part 9 of 9More from the specification

More from the specification
Magnetic Force on Charged Particles
  • A charged particle moving with velocity v perpendicular to uniform magnetic fields experiences a Lorentz force F = qvB, acting as a centripetal force.
Charge-to-Mass Ratio (q/m) and Deflection
  • In mass spectrometry, charged particles follow circular trajectories whose radius (r = mv / qB) depends on the charge-to-mass ratio.
    • (such as isotopes of boron or protons)
Velocity Selector with Crossed Fields
  • Perpendicular electric and magnetic fields between parallel charged plates exert equal and opposite forces (qE = qvB), transmitting only particles with velocity v = E/B.
Direction of Deflection for Opposite Charges
  • Positive particles (e.g. protons) and negative particles (e.g. electrons) deflect in opposite directions within the same magnetic field according to Fleming's left-hand rule.
Proton
  • Positive particle in the nucleus, relative charge +1 and relative mass 1.
Velocity
  • Rate of change of displacement.
Charge-to-mass ratio
  • Q/m, which determines the acceleration in a given field
Field lines
  • Lines showing the direction and strength of a magnetic field.
F = Bqv
What the symbols mean: F = force on the moving charge (N) · B = magnetic flux density (T) · q = charge (C) · v = speed (m s−1)

Key terms

TermMeaning
Magnetic flux densityThe strength of a magnetic field, measured in tesla (T).
Tesla (T)The SI unit of B: 1 N A⁻¹ m⁻¹.
Conventional currentDirection positive charge would move, from positive to negative terminal.
Fleming's left-hand ruleHand rule linking field, current and force directions.
CommutatorSplit-ring device that reverses the current in a motor coil every half turn.
Current balanceApparatus that measures B from the force on a current-carrying wire.

Avoid these mistakes

1
Using the total wire length instead of only the part inside the field.
2
Forgetting sin θ when the wire is not perpendicular to the field — a parallel wire feels no force.
3
Thinking the force is along the field or along the wire — it is perpendicular to both.
4
Using electron-flow direction instead of conventional current in the hand rule.
5
Treating tesla as a force unit — T is N A^{−1} m^{−1}.

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