# Charge redistribution

Electricity and Magnetism Level 5

Consider a neutral conducting sphere of radius $$R=1~\text{cm}$$. It is clear that if there are no other charges nearby, the electrostatic energy of the sphere is zero. However, if a charge $$q$$ is placed in the vicinity of the sphere, the charges on its surface redistribute and, as a consequence, the sphere acquires an electrostatic potential energy $$\Delta{U}$$. Determine the interaction energy $$\Delta{U}$$ in Joules among the charges on the surface of the sphere if a charge $$q=1~\mu \text{C}$$ is placed at a distance $$d=3~\text{cm}$$ from its center.

Details and assumptions

$k=\frac{1}{4\pi \epsilon_{0}}= 9\times 10^{9}~\text{m/F}$

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