Year 12 Physics Module 6: Electromagnetism IQ2: Motor Effect Lessons 7–10 45 min

Checkpoint 2: The Motor Effect

Test your understanding of the motor effect, forces between parallel conductors, torque on coils, DC motor design, and back emf. Covers displayed Lessons 8–12.

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Lesson 7

The Motor Effect

  • $F = BIL$ on current-carrying conductor
  • Right-hand palm rule for direction
  • Force between parallel current-carrying wires
Lesson 8

Forces Between Parallel Conductors

  • $F/l = \mu_0 I_1 I_2 / (2\pi d)$
  • Attractive for same-direction currents
  • Repulsive for opposite-direction currents
Lesson 9

Torque on a Current-Carrying Coil

  • $\tau = nBAI \cos \theta$
  • Split-ring commutator for DC motors
  • Radial magnetic field for smooth torque
Lessons 10 and 17

Motor Overview and DC Motor Depth

  • Back emf: $\varepsilon_{back} = k_e\omega$
  • AC induction motor: rotating stator field
  • Squirrel cage rotor and slip
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Essential Formulae, Motor Effect

$F = BIL$Motor effect force (perpendicular)
$\frac{F}{l} = \frac{\mu_0 I_1 I_2}{2\pi d}$Force per unit length between parallel wires
$\tau = nBAI \cos \theta$Torque on coil
$\varepsilon_{back} = k_e\omega$Back emf of a motor ($k_e$ is the motor constant)
$I = \frac{V - \varepsilon_{back}}{R}$Motor current with back emf
Key Terms
Motor effectForce on a current-carrying conductor in a magnetic field
CommutatorSplit-ring device that reverses current for continuous rotation
Back emfInduced voltage opposing supply voltage; increases with speed
Radial fieldCurved pole pieces keep B approximately parallel to the coil plane as it turns, so the torque stays nearly constant
Squirrel cageRotor with conducting bars shorted at ends; no brushes needed
SlipDifference between synchronous speed and rotor speed in induction motors
Multiple Choice, 10 Questions

1. A 0.50 m wire carries 4.0 A perpendicular to a uniform magnetic field of 0.20 T. The force on the wire is:

A0.20 N
B0.40 N ($F = BIL = 0.20 \times 4.0 \times 0.50$)
C0.80 N
D4.0 N

2. Two parallel wires carry currents in the same direction. The force between them is:

AAttractive
BRepulsive
CZero
DPerpendicular to both wires

3. A coil with 40 turns, area $3.0\times10^{-3}$ m², carries 2.5 A in B = 0.40 T. Maximum torque is:

A0.040 N m
B0.12 N m ($\tau = nBIA = 40 \times 0.40 \times 2.5 \times 3.0\times10^{-3}$)
C0.30 N m
DZero

4. In a DC motor, the split-ring commutator:

AIncreases the magnetic field
BReverses current every half-turn for continuous rotation
CReduces friction
DConverts AC to DC

5. A radial magnetic field in a DC motor is used to:

AKeep torque nearly constant throughout rotation
BReduce the current needed
CIncrease the number of turns
DReverse the magnetic field direction

6. A DC motor connected to 12 V has coil resistance 3.0 ohms. At full speed, back emf is 9.0 V. The running current is:

A4.0 A
B1.0 A ($I = (12-9)/3.0$)
C3.0 A
D7.0 A

7. The back emf of a DC motor is maximum when:

AThe motor is stalled
BThe motor is running at maximum speed
CThe current is maximum
DThe load is suddenly increased

8. An AC induction motor has no commutator because:

AIts rotor currents are induced by the rotating stator field, so no sliding contacts are needed
BIt uses permanent magnets
CThe rotor is connected directly to power
DThe AC supply already alternates, so no reversal is ever required

9. Two parallel wires 0.10 m apart carry currents I1 = 5.0 A and I2 = 3.0 A in opposite directions. The force per metre is:

A$1.5\times10^{-5}$ N/m (attractive)
B$3.0\times10^{-5}$ N/m (repulsive)
C$3.0\times10^{-4}$ N/m
D$1.5\times10^{-4}$ N/m

10. The torque on a coil is zero when:

AThe plane is parallel to the field
BThe plane is perpendicular to the field
CThe current is maximum
DThe coil has maximum area
Short Answer, 2 Questions

1. (4 marks) A DC motor has coil resistance 2.0 ohms and is connected to a 10 V supply. When running at full speed, the back emf is 8.0 V.

  • Calculate the current when the motor is running at full speed. (1 mark)
  • Calculate the current when the motor is stalled. (1 mark)
  • Explain why the stall current is much larger than the running current. (2 marks)

2. (4 marks) A rectangular coil with 80 turns and area $5.0\times10^{-3}$ m² carries a current of 3.0 A in a uniform magnetic field of 0.25 T.

  • Calculate the maximum torque on the coil. (2 marks)
  • Explain why a DC motor uses a radial magnetic field rather than a uniform field. (2 marks)
Answers

Multiple Choice: 1-B, 2-A, 3-B, 4-B, 5-A, 6-B, 7-B, 8-A, 9-B, 10-B

Short Answer 1: (a) I = (10-8)/2.0 = 1.0 A. (b) I_stall = 10/2.0 = 5.0 A. (c) At stall, back emf = 0, so the full 10 V drives current through the 2.0 ohm coil. At full speed, back emf of 8 V opposes the applied voltage, leaving only 2 V to drive current.

Short Answer 2: (a) tau_max = nBIA = 80 x 0.25 x 3.0 x 5.0x10^-3 = 0.30 N m. (b) With the angle measured from the coil plane, torque varies as cos theta and is zero when the plane is perpendicular to B. A radial field keeps B approximately parallel to the coil plane, maintaining nearly constant torque and smooth rotation.