IGCSE Physics 0625: Factors Affecting the Force in the Motor Effect

A student investigates the motor effect using a straight wire clamped so that it can be rotated between the flat pole pieces of a strong horseshoe magnet, carrying a current $I$ from a variable d.c. supply. The horseshoe magnet itself rests on a sensitive top-pan balance, so that (by Newton's third law) any force the field exerts on the wire is matched by an equal and opposite force on the magnet, which changes the balance reading, letting the student use the balance reading as a measure of the size of the force on the wire.

(a) With the wire held at right angles ( $90^\circ$ ) to the magnetic field, the student steadily increases the current $I$ in the wire from zero. State what happens to the size of the force on the wire as $I$ increases, and explain why. [2]

(b) The student then keeps the current constant, but slowly rotates the wire so that the angle between the wire and the magnetic field decreases from $90^\circ$ (wire at right angles to the field) towards $0^\circ$ (wire parallel to the field). Describe how the size of the force on the wire changes during this rotation, stating clearly the size of the force at each of the two extremes, $90^\circ$ and $0^\circ$ . [3]

(c) State two separate changes, other than increasing the current, that the student could make to increase the maximum force on the wire. [2]

Part (a): Increasing the current

As the current $I$ in the wire increases, the balance reading changes by a progressively larger amount, showing that the size of the force on the wire increases as the current increases.

This happens because the motor effect produces a bigger force whenever a bigger current flows through a conductor in a magnetic field of a given strength. Increasing the current increases the size of the force, with the field strength and the angle of the wire unchanged.

Part (b): Rotating the wire relative to the field

When the wire is at $90^\circ$ to the field (at right angles to it), it is cutting across the field lines as directly as possible, so the force on it is at its maximum.

As the student rotates the wire so the angle between the wire and the field decreases, the size of the force gradually decreases too.

By the time the wire has been rotated all the way to $0^\circ$ (that is, until the wire is lying parallel to the magnetic field) the force on the wire has fallen to zero. A current flowing parallel to the field experiences no force at all.

So over the rotation: force is maximum at $90^\circ$ , decreases steadily as the angle is reduced, and reaches zero at $0^\circ$ .

Part (c): Increasing the maximum force

Besides increasing the current, the maximum force on the wire (i.e. the force with the wire held at $90^\circ$ to the field) can be increased by, for example:

using a stronger magnet, which increases the strength of the magnetic field, or
increasing the length of wire within the field, so a greater length of current-carrying conductor experiences the field.

Any two of these changes are valid, since each increases the size of the motor-effect force independently of the current.

Final answers

(a) The force increases as $I$ increases. A larger current gives a larger motor-effect force for the same field.
(b) Force is maximum at $90^\circ$ (wire at right angles to the field), decreases as the wire is rotated towards parallel, and is zero at $0^\circ$ (wire parallel to the field).
(c) Any two of: use a stronger magnet; increase the length of wire within the field.