The d.c. motor

1. Overview

The d.c. motor is a device that converts electrical energy into kinetic energy (rotational motion) using the motor effect. This principle is fundamental to modern technology, powering everything from small cooling fans in computers to the powerful engines in electric vehicles.

Key Definitions

• Motor Effect: The force experienced by a current-carrying conductor when placed inside a magnetic field.
• Turning Effect (Torque): The rotational force that causes the coil in a motor to spin around its axis.
• Split-ring Commutator: A metal ring split into two halves that rotates with the coil to reverse the direction of the current every half-turn.
• Brushes: Stationary graphite or metal contacts that rub against the commutator to pass electrical current from the battery into the rotating coil.

Core Content

When a rectangular coil of wire is placed in a magnetic field and a current flows through it, the magnetic field of the wire interacts with the magnetic field of the magnets. This creates a force on each side of the coil (in opposite directions), resulting in a turning effect.

Increasing the Turning Effect

To make a motor spin faster or provide more power (torque), you can increase the turning effect. This is achieved in three ways:

1. Increase the number of turns on the coil: More loops of wire mean more current-carrying conductors are interacting with the magnetic field.
2. Increase the current: Using a higher voltage battery or a lower resistance wire increases the flow of charge.
3. Increase the strength of the magnetic field: Using stronger permanent magnets or moving the magnets closer to the coil.

Worked Example: Question: Motor A has 50 turns and a 2A current. Motor B has 100 turns and a 2A current. Which motor provides a stronger turning effect? Answer: Motor B. Because the number of turns is doubled while the current remains the same, the total magnetic force acting on the coil sides increases, resulting in a larger turning effect.

Extended Content (Extended Curriculum Only)

How the Motor Rotates

For a motor to keep spinning in the same direction, the forces acting on the sides of the coil must switch every half-turn ($180^\circ$). If they didn't, the coil would just oscillate back and forth.

1. Fleming’s Left-Hand Rule: Use this to determine the direction of the force. (Thumb = Force, Index = Magnetic Field N→S, Middle = Current + to -).
2. The Split-ring Commutator: This is the "switch." As the coil reaches the vertical position, the gaps in the split-ring lose contact with the brushes for a tiny fraction of a second. Momentum carries the coil forward. When the rings reconnect with the brushes, the current flows into the opposite side of the coil.
3. Continuous Rotation: By reversing the current every half-turn, the commutator ensures that the force on the left side of the motor is always "up" and the force on the right side is always "down," maintaining clockwise or anticlockwise rotation.

Variation in Turning Effect

Even if the magnetic force ($F=BIL$) is constant, the turning effect changes as the coil rotates:

• Maximum Torque: When the coil is horizontal (parallel to the field). The perpendicular distance from the pivot is greatest.
• Zero Torque: When the coil is vertical. The forces act directly up and down through the center of the coil, providing no "leverage."

Key Equations

While specific torque calculations are often not required, the relationship is defined by: $F = B \times I \times L$

• $F$: Force (Newtons, N)
• $B$: Magnetic Field Strength (Tesla, T)
• $I$: Current (Amperes, A)
• $L$: Length of wire in the field (Metres, m)

Note: The total turning effect is also proportional to the number of turns ($N$) and the width of the coil.

Common Mistakes to Avoid

• ❌ Wrong: Thinking fewer turns of wire helps the motor by reducing electrical resistance.
  • ✓ Right: More turns always increase the motor effect because each turn experiences its own force, which adds up.
• ❌ Wrong: Thinking that the magnetic force on the wire changes as it spins.
  • ✓ Right: The force remains constant, but the turning effect (moment) changes because the distance from the pivot changes with the angle.
• ❌ Wrong: Confusing the brushes and the commutator.
  • ✓ Right: The Brushes stay still; the Commutator spins.
• ❌ Wrong: Thinking that reversing both the battery and the magnets will change the motor's direction.
  • ✓ Right: Reversing both variables cancels the change out, and the motor will spin in the same direction as it did originally.

Exam Tips

1. Check the symmetry: Remember that the turning effect at $45^\circ$ is exactly the same as at $135^\circ$ (positions 2 and 4 in many diagrams) because they are mirror images relative to the magnetic field.
2. Explain the "Why": If asked how to reverse the motor, state: "Reverse the direction of the current OR reverse the direction of the magnetic field." Do not say "both" unless you want it to keep spinning the same way!
3. Left-Hand Rule: Always use your Left Hand for motors (where current creates motion). Many students accidentally use their right hand and get the direction backwards.