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20.3Magnetic Fields

Forces on Currents and the d.c. Motor — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 5 of 5 1 quiz

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Lesson summary

Describe an experiment showing the force on a current-carrying conductor in a magnetic field.Force on a wire at right angles to a fieldF = BIL (N = T × A × m).If the wire makes angle θ with the fieldF = BIL sin θ; F = 0 when parallel.Force on a charge moving at right angles to a …

  • Electrons are negative
  • Fleming's left-hand rule
  • Motor effect
  • Magnetic flux density
  • d.c. motor
  • Commutator

Part 1 of 7Key ideas

1Force on a wire at right angles to a field
F = BIL (N = T × A × m).
2If the wire makes angle θ with the field
F = BIL sin θ; F = 0 when parallel.
3What the symbols mean:
Force on a charge moving at right angles to a field: F = Bqv (N = T × C × m/s).
What the symbols mean: F = force on the moving charge (N) · B = magnetic flux density (T) · q = charge (C) · v = speed (m s−1)
4
Force is perpendicular to both the current and the field (Fleming's left-hand rule).
5
Reversing either current or field reverses the force.
6
A d.c. motor turns faster with larger current, stronger magnets, more turns.
7Electrons are negative
Electrons are negative for Fleming's rule, conventional current is opposite to the electron velocity.
8
Turning effect on the coil is greatest when the coil plane is parallel to the field and zero when perpendicular.

Part 2 of 7Learning objectives

1
Describe an experiment showing the force on a current-carrying conductor in a magnetic field.
2
Apply Fleming's left-hand rule to find force direction.
3
Use F = BIL and F = Bqv.
4
Explain the turning effect on a coil and the operation of a d.c. motor with a commutator.
5
Describe how to increase the turning effect and how a loudspeaker works.

Part 3 of 7Essential knowledge

1
20.3 Forces on Currents and the d.c. Motor concept map: Force on a wire at right angl, If the wire makes angle θ wit, Electrons are negative, Fleming's left-hand rule, Motor effect
Visual guide to the key ideas explained in this lesson.
2
The motor effect arises because the magnetic field of the current interacts with the external magnetic field; the resultant field is stronger on one side of the wire, and the wire is pushed towards the weaker side.
3
A simple demonstration is a copper rod resting on two metal rails between the poles of a magnet: when current flows, the rod rolls along the rails. Reversing current or field reverses the direction.
4Fleming's left-hand rule
First finger for Field (N→S), seCond finger for Current (+→−), thuMb for Motion (force).
5
The size of the force increases with current, field strength and length of wire in the field: F = BIL for a wire perpendicular to the field.
6
In a rectangular coil in a field, the sides perpendicular to the field carry current in opposite directions, so the forces are in opposite directions and produce a turning effect (moment).
7
The turning effect is increased by increasing the number of turns, the current, and the strength of the field (and the area of the coil).
8
A split-ring commutator reverses the current direction in the coil every half-turn so that the force on each side always acts to turn the coil the same way. Brushes maintain contact with the rotating commutator.
9
Practical motors use curved (radial) magnets, many coils at different angles and a soft-iron core to give a smoother, larger turning effect.
10
A beam of charged particles moving across a magnetic field is deflected; for a uniform field at right angles the path is a circle. Positive and negative charges are deflected in opposite directions.
11
In a loudspeaker, alternating current in the coil causes a force that changes direction at the frequency of the signal, so the cone vibrates and produces sound waves.
12
Two parallel wires carrying current in the same direction attract; in opposite directions they repel.

Part 4 of 7Process & sequence

1
Current flows into the coil through a brush and the commutator.
2
The two sides of the coil carry current in opposite directions across the magnetic field.
3
By Fleming's left-hand rule, one side is pushed up and the other down: a turning effect.
4
The coil rotates; when it is vertical the brushes cross the gap in the split ring.
5
The commutator reverses the current in the coil every half-turn.
6
Forces now keep turning the coil the same way; momentum carries it past the vertical, so rotation is continuous.

Using Fleming's left-hand rulewrite these steps in this order; each step is a marking point.

1
Point the first finger along the field, from N to S.
2
Point the second finger along the conventional current (+ to −).
3
Keep thumb, first and second fingers mutually at right angles.
4
The thumb gives the direction of the force (motion).
5
If either field or current is reversed, the force is reversed.

Part 5 of 7Worked examples

0.12 N
A 0.25 m wire carries a current of 4.0 A at right angles to a field of 0.12 T. Find the force on it.
  • F = BIL = 0.12 T × 4.0 A × 0.25 m = 0.12 N.
    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
An electron (q = 1.6 × 10−19 C) moves at 3.0 × 106 m/s perpendicular to a 0.050 T field. Find the magnetic force.
  • F = Bqv = 0.050 × 1.6 × 10−19 × 3.0 × 106 = 2.4 × 10−14 N, at right angles to its velocity.
0.30 m
A wire in a field of 0.40 T experiences a force of 0.30 N when it carries 2.5 A perpendicular to the field. Find the length of wire in the field.
  • L = F/(BI) = 0.30/(0.40 × 2.5) = 0.30 m.

Part 6 of 7Summary

1
A current in a magnetic field experiences a force (the motor effect).
2
Direction from Fleming's left-hand rule.
3
Magnitude: F = BIL, largest when wire is perpendicular to the field.
4
The split-ring commutator reverses the current every half-turn to keep the motor spinning.
5
Moving charges are deflected at right angles to both velocity and field.

Part 7 of 7Compare: Compare

Factors affecting the force and motor speed
ChangeEffect
Increase currentLarger force; motor turns faster
Stronger magnetic fieldLarger force; motor turns faster
More turns on coilLarger turning effect
Reverse current OR fieldForce reverses; motor reverses
Reverse bothForce direction unchanged
Wire parallel to fieldNo force
Left-hand versus right-hand rules
RuleUseFinger meanings
Fleming's left-hand ruleMotor effect (force on current)Thumb = force/motion, First = field, seCond = current
Right-hand grip ruleField direction around currentThumb = current, fingers = field
Fleming's right-hand ruleGenerator (induced current)Thumb = motion, First = field, seCond = induced current

Key terms

Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Motor effect · Fleming's left-hand rule · Magnetic flux density · Tesla (T) · d.c. motor · Commutator · Brushes · Turning effect (torque) on a coil · Force on a moving charge · Loudspeaker · Beam of charged particles
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1
the commutator changes a.c. to d.c. in a motorthe commutator reverses the current in the coil every half-turn so the coil keeps turning the same way.
2
the magnets repel the wirethe magnetic field of the current interacts with the magnet's field, producing a force on the wire.
3
use the right hand for motorsuse Fleming's left-hand rule for the motor effect.
4
a wire in a field always has a force on itthere is a force only if the current has a component perpendicular to the field.
5
use electron flow for the second fingerthe second finger shows conventional current.

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