Consider a straight conductor of length L carrying a steady current I as it is rotated uniformly through all possible orientations within a uniform magnetic field of magnitude B. The angle between the conductor and the magnetic field is denoted by θ.
a. (a) Write the expression for the instantaneous magnetic force F acting on the conductor as a function of θ.
b. (b) Derive an expression for the average magnitude of the force, ⟨F⟩, experienced by the conductor.
c. (c) Show that the average value obtained in part (b) can be written as ⟨F⟩=π2ILB, and briefly interpret the physical significance of this result in the context of practical devices where the conductor sweeps through all orientations.