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Question

The electric field at 20 cm from the centre of a uniform charged non - conducting sphere of radius 10 cm is E. Then at a distance of 5 cm from the centre it will be :

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Solution


For a non conducting sphere containing a distributed charge Q and of rations R the electric field in given at a distance r
E=⎪ ⎪ ⎪⎪ ⎪ ⎪KQr2,when r>R(outside)pr3to,when r>R(inside)and herep=Qv[charge density]
at a distance r=20 cm, field is E (r>R) where R=10 cm (Radius of sphere)
E=KQ2O2Q=400EK=1600πϵ0E (as K=14πϵ0)
now volume of sphere V=43πR3
So at a distance r=5 cm, (r<R), inside sphere :-
E=pr3ϵ0=Qrv3ϵ0
=1600πϵ0E×543π×103×3×ϵ0=2000E1000=2E
E=2E (Ans)

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