Quick questions on Magnetic force on a current and the DC motor: VCE Physics Unit 3

A straight wire of length $L$ carrying current $I$, with $n$ turns or wires, in a uniform field $B$ perpendicular to the current, feels a force:

Consider a rectangular coil of $n$ turns, width $w$ and length $L$, carrying current $I$ in a uniform field $B$ parallel to the plane of the coil. The forces on the two long sides are equal in magnitude ($F = n B I L$) but opposite in direction (one up, one down). These forces form a couple that rotates the coil about its axis.

A simple DC motor consists of:

State the force on a current-carrying conductor in a magnetic field and explain the role of the split-ring commutator in a DC motor. [3 marks]

A coil of $50$ turns and length $0.10$ m carries $2.0$ A in a $0.5$ T field. Calculate (a) the force on one side, and (b) the torque if the coil width is $0.08$ m. [4 marks]

Refer to the Melbourne tram traction motor. (a) Calculate the force on a coil side of $L = 0.3$ m at $I = 400$ A, $B = 0.8$ T, $N = 60$. (b) Determine the torque if armature radius is $0.2$ m.