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

Answer

A

Explanation

The charge on the sphere is
`=` Area `xx` surface charge density
`=4piR^(2)xxsigma`
Therefore for the hemisphereical
shell, charges `(q)=2piR^(2)sigma`
The intensity of the electric field near a conductor is
`E=(sigma)/(2epsilon_(0))` but`E=F/q`
`F=Eq=((sigma))/((2epsilon_(0)))xx2piR^(2)sigma=(pisigma^(2)R^(2))/(epsilon_(0))`
`:.F prop (sigma^(2)R^(2))/(epsilon_(0))`