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A conducting bar of length $L$ rotates at an angular frequency $\omega$ in a uniform, perpendicular magnetic field as shown.

a) Find the potential developed between the central end of the rod and a point at radius $r$ on the rotating rod.

b) Find the field associated with this potential difference (magnitude and direction) at the radius $r$.

c) Discuss the qualitative distribution of charge in the rod, assuming that it is in equilibrium (has been rotating for a long time).