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A point charge q is brought to a position a distance d away from an infinite plane conductor held at zero potential. Using the method of images, find: (a) the surface-charge density induced on the plane, and plot it: (b) the force between the plane and the charge by using Coulomb's law for the force between the charge and its image: (c) the total force acting on the plane by integrating σ^2 / 2 ϵ0 over the whole plane: (d) the work necessary to remove the charge q from its position to infinity;
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