A uniformly charged thin spherical shell of radius R carries uniform surface charge density of `sigma` per unit area. It is made of two hemispherical shells, held together by pressing them with force F. 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

Electrical force per unit area ` = (1)/(2) epsi_(0) E^(2) = (1)/(2) epsi_(0) ((simga)/(epsi_(0)) (pi R^(2)))`
Protected area ` = pi R^(2) " "therefore ` Net electrical force ` = ((sigma^(2))/(2 epsi_(0)) (pi R^(2)))`
In equilibrium, this force should be equal to the applied force.
`therefore " " F = (pi sigma^(2) R^(2))/(2 epsi_(0)) or F prop (simga^(2) R^(2))/(epsi_(0))`