(Solution) - Use Green s reciprocity theorem Prob 3 43 to solve the follow -(2025 Original AI-Free Solution)

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Use Green's reciprocity theorem (Prob. 3.43) to solve the following two problems.
(a) Both plates of a parallel-plate capacitor are grounded, and a point charge q is placed between them at a distance x from plate 1. The plate separation is d. Find the induced charge on each plate.
(b) Two concentric spherical conducting shells (radii a and b) are grounded, and a point charge q is placed between them (at radius r). Find the induced charge on each sphere.