Explain with a neat labelled diagram how the magnetic forces on a… - Vidyadip

Question

Explain with a neat labelled diagram how the magnetic forces on a current loop produce rotary motion as in an electric motor.

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Answer

Consider a current-carrying rectangular loop $A B C D$, within a uniform magnetic field $\frac{mg}{a B}$, from below figure. Lead wires and commutator are not shown for simplicity. The coil is free to rotate about a fixed axis. Suppose the sides $A B$ and $C D$ are perpendicular to the field direction.

The magnetic force on each segment act at the centre of mass of that segment. The direction of the force on each segment can be found using the right hand rule for the cross product or from Fleming’s left hand rule.
The magnetic forces on the short sides AD and CB are, in general, equal in magnitude, opposite in direction and have the same line of action along the rotation axis. Hence, these forces cancel out and does not produce any torque. The magnetic forces on the long sides AB and CD are also equal in magnitude and opposite in direction but their lines of action are different. Hence, these forces constitute a couple and tend to rotate the coil about the central axis.
A commutator (not shown) reverses the direction of the current through the loop every half-revolution so that the torque always acts in the same direction.

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