Know that a current-carrying coil in a magnetic field may experience a turning effect and that the turning effect is increased by increasing: (a) the number of turns on the coil (b) the current (c) the strength of the magnetic field

4.5.5 The d.c. Motor

What is a d.c. motor?

A d.c. motor is a device that turns electrical energy into mechanical motion. Picture a tiny wheel (the rotor) that spins when you push a button. Inside the wheel is a coil of wire that carries current. When this current‑carrying coil sits inside a magnetic field, it feels a force that tries to rotate it. This is the turning effect.

Why does the coil turn?

The force on a current‑carrying wire in a magnetic field is given by the Lorentz force law:

\$\mathbf{F}=I\,\mathbf{L}\times\mathbf{B}\$

For a coil, the forces on opposite sides push in opposite directions, creating a torque that makes the coil spin.

The torque equation

The torque (turning effect) on a coil is:

\$\tau = N\,I\,A\,B\,\sin\theta\$

  • \$N\$ – number of turns in the coil
  • \$I\$ – current through the coil (amps)
  • \$A\$ – area of the coil (m²)
  • \$B\$ – magnetic field strength (teslas)
  • \$\theta\$ – angle between the coil plane and the magnetic field (max torque when \$\theta = 90^\circ\$)

How to increase the turning effect

  1. More turns (\$N\$) – Think of winding a coil like wrapping a rubber band around a stick. The more loops, the stronger the pull.
  2. Higher current (\$I\$) – Like turning up the volume on a speaker; more electrons flow, more force.
  3. Stronger magnetic field (\$B\$) – Imagine placing the coil near a powerful magnet; the magnetic “push” is stronger.

Quick Reference Table

FactorEffect on TorqueAnalogy
\$N\$ – Number of turnsDirectly proportional (\$\uparrow\$)More loops = stronger pull, like a stronger rope
\$I\$ – CurrentDirectly proportional (\$\uparrow\$)More electrons = stronger push, like turning up a fan
\$B\$ – Magnetic fieldDirectly proportional (\$\uparrow\$)Stronger magnet = stronger force, like a magnet pulling a metal nail

Real‑world example: A toy electric fan

When you press the button on a toy fan, the battery sends current through a coil inside the fan. The coil is placed in the fan’s magnetic field, so it starts spinning. If you replace the coil with one that has more turns, or use a stronger battery (higher \$I\$), the fan spins faster. If you also use a stronger magnet, the fan will spin even quicker. This is exactly how the torque equation works in practice.

Key Takeaway

The turning effect of a d.c. motor increases when you increase the number of turns, the current, or the magnetic field strength. All three factors multiply together in the torque formula.