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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?

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? 

Grade:Upto college level

1 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
10 years ago

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/3εo - pr/3εo = p(R-r)/3εo

= pa/3εo (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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