A non-conducting solid sphere has uniform volume charge density ρ. A spherical cavity is carved out whose centre is displaced from the original sphere's centre by a vector d. The cavity lies completely inside the original sphere. The electric field at every point inside the cavity is:
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Question

A non-conducting solid sphere has uniform volume charge density ρ. A spherical cavity is carved out whose centre is displaced from the original sphere's centre by a vector d. The cavity lies completely inside the original sphere. The electric field at every point inside the cavity is:

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G1 Physics · Accepted Answer

Superpose the original uniformly charged sphere and a sphere of charge density -ρ occupying the cavity. For a point inside the cavity, E = ρr/(3ε₀) - ρr′/(3ε₀). Since r = d+r′, E = ρd/(3ε₀), independent of position.