Exercise 6. A thin, perfectly insulated, wire is bent into the shape of a circle of radius a. a. Assuming the temperature, u, in the wire at any point obeys the one-dimensional heat equation (with respect to arc length), show that, in terms of the polar coordinate angle 0, the temperature at any point on the wire satisfies Ut = 2 (9) Ugg- b. Assuming a given initial temperature distribution f(0) around the ring, separate vari- ables and find an expression for the temperature at any point in the ring at any later time.