direction of twist So the repulsion between the two spheres causes the wire to twist the rod counterclockwise and stop at some point when the forces...

Well, for a torsion wire, the formula is the angular equivalent: τ = -κθ, where this time κ is an "angular spring constant" (called the "torsion coefficient"), which has units of Nm per radian.

(a) A given Coulomb torsion balance has a rod of length 10.0 cm and uses a torsion wire with a torsion coefficient of 1.50 Nm/rad. The fixed sphere and the free sphere are carefully set up to just be touching, with no torque on the wire. A third identical sphere is charged up to a total charge of -1.50 μC, inserted into the apparatus with an insulating rod and allowed to touch the two spheres in the torsion balance. The third sphere is then retracted. The two spheres in the torsion balance now repel each other and the wire will twist. Calculate the angle of twist (in degrees). Note: I could not find good estimates as to the actual values Coulomb himself would have used, so the numbers given, although reasonable, are made up and not meant to be historically accurate. (6 marks)

(b) An identical neutral metal sphere is inserted into the apparatus and allowed to contact the fixed sphere, and is then removed. What is the angle of separation Coulomb would have measured now? (1 mark)

(c) Draw a free-body diagram for the free sphere and briefly explain it. (1 mark)