A thin spherical shell radius of `R` has of charge `Q` unfromily distributed on it.At the centre of the shell ,a negative point charge `-q` is placed.IF the shell is cut into two identical hemisphere still equlibrium is maintained .Then find the relation between `Q` and `q`?

Explanation

Here the outward electric pressure at everypoint on the shell due to its own charge is
`P_(1)=(sigma^(2))/(2epsilon_(0))=(1)/(2epsilon_(0))((Q)/(4pir^(2)))^(2),P_(1)=(Q^(2))/(32pi^(2)epsilon_(0r^(4)))`
Due to `-q` the electric filed on the surface ofthe shell is
`E=(1)/(4piepsilon_(0))(q)/(r^(2))`
This electric fields pulls every point of the shell in inward directions.Theinward pressure on the surface to the shell due to the negative charge is
` P_(2)=sigmaE,=((Q)/(2pir^(2)))((1)/(4piepsilon_(0))(q)/(r^(2)))=(Qq)/(16pi^(2)epsilon_(0)r^(4))`
for equilibrium of the hemisphere shells `P_(2) geP_(1)`
or `(Qq)/(16pi^(2)epsilon_(0)r^(4)) ge (Q^(2))/(32pi^(2)epsilon_(0)r^(4)), " " Q ge(Q)/(2)`