a spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume. the electric field inside the emptied space is non-zero and uniform.how this can be proved using superposition principle?

Dear Nandan

assume in the cavity charge density p and -p.

let position of point from complete sphere is R vector and from cavity centre is r vector

net elec field= pR/3ε_o - pr/3ε_o = p(R-r)/3ε_o

= pa/3ε_o (from vector addition)   

where a vector is from centre of sphere to centre of cavity. so we take any point inside the cavity elec field will be pa/3ε and it is independent of position of point in the cavity. hence uniform.

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IIT Delhi

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