In one line
A DC motor works because a current-carrying conductor placed in a magnetic field experiences a force \( F = BIl \), and the commutator keeps this force producing torque in one direction.
Explained simply
Put a wire carrying current between the poles of a magnet and it jumps sideways. Wrap many such wires on a drum that can turn, and the sideways pushes on opposite sides form a twisting force, so the drum spins. That is a motor: electrical energy in, mechanical rotation out.
Technically, the field winding (or permanent magnets) produces the main flux. Armature conductors carrying current experience force \( F = BIl \); conductors under a N pole and under a S pole carry opposite currents, so their forces add up to a torque. Direction is given by Fleming's left-hand rule: forefinger = field, middle finger = current, thumb = motion (force).
How it works
- DC supply is connected to the field winding and, through brushes and commutator, to the armature.
- Field flux \( \phi \) is set up between the poles.
- Armature conductors carry current; each experiences a force; together these give torque \( T \propto \phi I_a \).
- As a conductor passes from one pole to the next, the commutator reverses its current, so the torque stays in the same direction and rotation is continuous.
- As the armature rotates, its conductors cut flux and a back EMF \( E_b \) is induced, opposing the supply. So \( V = E_b + I_aR_a \).
Key formula
\( F = BIl, \quad T \propto \phi I_a, \quad V = E_b + I_aR_a \)
\( F \) = force on one conductor (N), \( B \) = flux density (T), \( I \) = conductor current (A), \( l \) = active length (m), \( T \) = torque (N·m), \( \phi \) = flux per pole (Wb), \( I_a \) = armature current (A), \( V \) = supply voltage (V), \( E_b \) = back EMF (V), \( R_a \) = armature resistance (\( \Omega \)).
Quick example
A toy car motor: a small permanent-magnet DC motor runs from two AA cells. Reversing the battery reverses the armature current and so the direction of rotation, exactly as Fleming's left-hand rule predicts.
Common mistakes
- Using Fleming's right-hand rule for a motor (right-hand rule is for generators).
- Saying the commutator converts AC to DC in a motor; in a motor it reverses current in the conductors so torque stays unidirectional.
- Forgetting back EMF in the voltage equation.
How MU asks it
Numericals are not expected in this module (as per the MU syllabus), so questions are theory. Typical: "Explain the principle of operation of a DC motor" (5 marks). For full marks draw a two-pole motor with a conductor and force directions, state \( F = BIl \) and Fleming's left-hand rule, explain the role of the commutator, and write \( V = E_b + I_aR_a \) and \( T \propto \phi I_a \).