Class 10 > Unit # 16: Electromagnetism > Magnetic Torque & Working of DC Motor

Talha's Physics Academy

Torque on a Rectangular Coil and Working of DC Motor

Torque on a Current-Carrying Rectangular Coil

"When a current passes through a coil placed in a magnetic field, equal and opposite parallel forces act on the opposite sides of the coil, producing a couple that exerts a turning effect (torque) on the coil."

Consider a rectangular coil placed in a uniform magnetic field of strength $B$ such that it is free to rotate about an axis. When a current $I$ flows through the coil, perpendicular forces of magnitude $F = BIL$ act on the opposing conductor arms, creating a couple.

Mathematical Derivation

The basic torque ($\tau$) produced by the couple is given by the product of the force and the perpendicular distance between their lines of action:

$$\tau = F \times \text{width}$$

Since $F = BIL$ and $L \times \text{width} = A$ (area of the coil), the maximum torque when the plane of the coil is parallel to the field is:

$$\tau = BIA$$

If the plane of the coil makes an angle $\alpha$ with the magnetic field $B$, the effective perpendicular distance is reduced by a factor of $\cos\alpha$:

$$\tau = BIA \cos\alpha$$

If the coil consists of $N$ turns, the total torque is multiplied by $N$:

$$\tau = NIAB \cos\alpha$$

Note: The torque is maximum when the plane of the coil is parallel to the magnetic field ($\alpha = 0^\circ$), and zero when the plane is perpendicular to the field ($\alpha = 90^\circ$).

Working Principle of a D.C. Motor

"A D.C. Motor is an electromechanical device that converts electrical energy into mechanical energy."

In terms of construction, a D.C. motor is structurally similar to a D.C. generator, but it operates in reverse: electrical energy is supplied as input to produce mechanical rotation as output.

Turning Effect in a D.C. Motor

The operation relies directly on the turning effect experienced by a current-carrying coil in a magnetic field:

1. Sides Parallel to Field ($BC$ and $DA$): These sides carry current in directions parallel to the magnetic field lines, so no magnetic force is exerted on them.
2. Sides Perpendicular to Field ($AB$ and $CD$): These sides experience equal and opposite magnetic forces whose directions can be determined using Fleming's Left-Hand Rule or the Right-Hand Slap Rule.
3. Couple Formation: The opposing forces on sides $AB$ and $CD$ form a couple, generating a continuous turning effect that rotates the coil. These forces arise from the combination of the current's magnetic field and the external permanent magnetic field, creating resultant catapult fields around the coil.

Fig: Basic structure of a DC motor showing armature coil, permanent magnets, and force vectors.

© 2026 Talha's Physics Academy. All rights reserved.