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

Chapter 11, Problem 7

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Let u represent the electrostatic potential between two concentric metal spheres of radii R1 and R2 (R1 < R2). The potential of the inner sphere is kept constant at V1 volts, and the potential of the outer sphere is 0 volts. The potential in the region between the two spheres is governed by Laplaces equation, which, in this particular application, reduces to d2u dr2 + 2 r du dr = 0, R1 r R2, u(R1) = V1, u(R2) = 0. Suppose R1 = 2 in., R2 = 4 in., and V1 = 110 volts. a. Approximate u(3) using the Linear Shooting Algorithm. b. Compare the results of part (a) with the actual potential u(3), where u(r) = V1R1 r R2 r R2 R1 .