Surface density of charge on a sphere of radius R in terms of electric intensity E at a distance in free space is
`(epsi_(0)` = permittivity of free space)

Options

A. `epsi_(0)E((R)/(r))^(2)`
B. `(epsi_(0)ER)/(r^(2))`
C. `epsi_(0)((r)/(R))^(2)`
D. `(epsi_(0)Er)/(R^(2))`

Answer

C

Explanation

This is based on the formulae of E and `sigma`.
for a sphere`, E=(1)/(4piepsi_(0))(Q)/(r^(2))` (in free space K=1)
`therefore Q=4piepsi_(0)Er^(2)` . . . (1)
and surface charge density `sigma=(Q)/(4piR^(2))`
`therefore sigma=(4piepsi_(0)Er^(2))/(4piR^(2))=epsi_(0)E((r)/(R))^(2)`