A thin sphericalshell radiusof r has a charge Q uniformly distributedon it . At the centreof theshell , a negativepointcharge-q is palced . If the shell is cutintotwo identical hemisphere , stillequibrium is mainated . Then find therelation betweenQ and q ?

A thin sphericalshell radiusof r has a charge Q uniformly distributedo

1.	A thin sphericalshell radiusof r has a charge Q uniformly distributedon it . At the centreof theshell , a negativepointcharge-q is palced . If the shell is cutintotwo identical hemisphere , stillequibrium is mainated . Then find therelation betweenQ and q ?
Answer» Solution :Here theoutwardelectricpressureat everypointon the shell dueto itsown chargeis . `P_(1) = (sigma^(2))/(2in_(0)) = (1)/(2 in_(0)) ((Q)/(4pir^(2)))^(2)` `P_(1)= (Q^(2))/(32 pi^(2) in_(0) r^(4))` Due to -q , the electricfieldon the surface of the shell is `E = (1)/( 4pi in_(0)) (q)/(r^(2))` Thiselectric FIELD pallseverypointof the shell in inward direction . Theinward pressureon the surface OFTHE shelldue tothe negative chargeis `P_(2) = sigma E ` ` = ((Q)/(4pi r^(2)))((1)/(4pi in_(0))(q)/(r^(2))) = (Qq)/(16pi^(2) in_(0)r^(4))` For equilibrium of the hemispherical shells `P_(2) geP_(1)`or `(Qq)/(16pi^(2) in_(0) r^(4)) GE (Q^(2))/(32 pi^(2) in_(0) r^(4))` `q ge (Q)/(2)` .