Quick questions on Magnetic force on conductors: WACE Year 12 Physics Unit 3

A length $L$ of wire carrying current $I$ in a field $B$ feels a force

Use the right-hand rule: point the fingers in the direction of the conventional current, curl toward the field, and the thumb (or palm push) gives the force. An equivalent statement points the fingers along the current and the palm along the field so the thumb shows the force. State the result as a clear direction such as "into the page" or "upward".

In a rectangular loop in a field, the two sides carrying current perpendicular to the field feel equal and opposite forces. These do not cancel as a turning effect because they act on opposite sides of the axis, so they produce a torque that rotates the loop. The torque is maximum when the loop plane is parallel to the field and zero when the plane is perpendicular (the forces then act along the same line).

A single wire experiences $F=BIL\sin\theta$, but a coil of $N$ turns multiplies the effect, since each turn feels the force, so the total turning effect on a loop scales with $N$. This is why real motors use many-turn coils and why the torque on a coil is often written as proportional to $NBIA$, where $A$ is the loop area. Increasing the number of turns, the current, the field strength or the coil area all raise the torque, which gives four practical design levers for a more powerful motor. The same four factors appear (as a rate of change) when the device is run in reverse as a generator, which is why the motor and generator are so closely linked.