A uniformly charged thin spherical shell of radius R carries uniform surface charge denisty of `isgma` per unit area. It is made of two hemispherical shells, held together by presisng them with force F(see figure). F is proportional to

Options

A. `(1)/(epsi_(0))sigma^(2)R^(2)`
B. `(1)/(epsi_(0))sigma^(2)R`
C. `(1)/(epsi_(0))(sigma^(2))/(R)`
D. `(1)/(epsi_(0))(sigma^(2))/(R^(2))`

Answer

A

Explanation

the charge on the sphere
=Area`xx`Surface charge density`=4piR^(2)xxsigma`
`therefore`For the hemispherical shell, charge `(q)=2piR^(2)sigma`
The intensity of the electric field near a conductor is
`E=(sigma)/(2epsi_(0))` but `E=(F)/(q)`
`therefore F=Eq=((sigma)/(2epsi_(0)))xx2piR^(2)sigma=(pisigma^(2)R^(2))/(epsi_(0))`
`therefore Fprop(sigma^(2)R^(2))/(epsi_(0))`