Solved: Let u represent the electrostatic potential between two concentric metal spheres

Chapter 11, Problem 6

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Let u represent the electrostatic potential between two concentric metal spheres of radii R\ and R2 (R] < Ri)- The potential of the inner sphere is kept constant at V\ volts, and the potential of the outer sphere is 0 volts. The potential in the region between the two spheres is governed by Laplace's equation, which, in this particular application, reduces to d 2 u 2 du -^ + - = 0, R] < r < R2, u(R\) = V], u(R2) = 0. dr- r dr Suppose R\ 2 in., R2 4 in., and V, = 110 volts. a. Approximate w(3) using the Linear Shooting Algorithm. b. Compare the results of part (a) with the actual potential m(3), where ViR] / R7 -r uir) = R2 R\