Three point charges (q, ?2q, q) are located in a straight line with separation a and with the middle charge (?2q) at the origin of a grounded conducting spherical shell of radius b, as indicated in the sketch.

(a) Write down the potential of the three charges in the absence of the grounded sphere. Find the limiting form of the potential as a ? 0, but the product qa² = Q remains finite. Write this latter answer in spherical coordinates.

(b) The presence of the grounded sphere of radius b alters the potential for r b. Use linear superposition to satisfy the boundary conditions and find the potential everywhere inside the sphere for r a. Show that in the limit a ? 0,

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