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Consider a grounded conducting sphere of radius a in the presence of a point charge q...

Consider a grounded conducting sphere of radius a in the presence of a point charge q a distance d away from the center of the sphere.

a)Show that the electric field E is everywhere normal to the surface of the sphere.

b)Calculate the induced charge per unit area on the surface of the sphere.

c)Show that the total induced charge is -qa/d.

d)Calculate the total force between the point charge and the sphere.

e)Show that your solution satisfies Laplace’s equation.

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