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Find V and E at : (Q is a point charge kept at the centre of the non-conducting neutral thick sphere of inner radius 'a' and outer radius 'b') (dielectric constant =in_(r)) (i) 0 lt r lt a "" (ii) a le r lt b "" (iii) r ge b |
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Answer» Solution :`-q` and `+q` charge will INDUCE on inner and outer surface RESPECTIVELY `E (0ltrlta)=(KQ)/(r^(2))` `E(r ge B)=(KQ)/(r^(2))` `E(a le r lt b) = (KQ)/(r^(2))-(Kq)/(r^(2))=(KQ)/(in_(r)r^(2))` `q=Q.(1-(1)/(in_(r))) , V(r ge b) = (KQ)/(r)` `(a le r le b) V_(A)=V_(P)+UNDERSET(b) overset(r)int (KQ)/(in_(r)r^(2))(-dr)=(KQ)/(b)+(KQ)/(in_(r))((1)/(r)-(1)/(b))` `V(r le a) " " V_(B)=5V_(c)+ underset(a)overset(r)int (KQ)/(r^(2))(-dr)=(kQ)/(b)+(kQ)/(in_(r))((1)/(a)-(1)/(b))+kQ((1)/(r)-(1)/(a))` |
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