The electric field intensity in free space at a distance 'r' outside a charged conducting sphere of radius 'R' in terms of surface charge density `sigma` is

Options

A. `(sigma)/(epsi_(0))[(R)/(r)]^(2)`
B. `(epsi_(0))/(sigma)[(R)/(r)]^(2)`
C. `(R)/(r)[(sigma)/(epsi_0)]^(2)`
D. `(R)/(sigma)[(r)/(epsi_(0))]^(2)`

Answer

A

Explanation

The electric field intensity at a point at a distance r outside
a charged conducting sphere is `E=(1)/(4piepsi_(0))(q)/(r^(2))` . .. (1)
where `r gt R`.
But surface charge density `(sigma)` of the sphere is
`sigma=(q)/(4piR^(2))" "therefore q=4piR^(2)sigma`
From (1), `E=(1)/(4piepsi_(0))(4piR^(2)sigma)/(r^(2)) =(sigma)/(epsi_(0))[(R)/(r)]^(2)`