Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field `|vecE(r)|` and the electric potential V (r) with the distance r from the center, is best represented by which graph?

Options

A.
B.
C.
D.

Answer

D

Explanation

For inside points, `( r le R) , " " E = 0 " " ` V = constnat = `(1)/(4 pi epsi_(0)) (q)/(R)`
For outside points `( r ge R) " "E = (1)/(4 pi epsi_(0)) .(q)/(r^(2)) or E prop (1)/(r^(2)) and V = (1)/(4 pi epsi_(0) ) (q)/(r) or V prop (1)/(r)`
on the surface `(r = R) , V = (1)/(4 pi epsi_(0)) (q)/(R) rARr E = (1)/(4 pi epsi_(0)) .(q)/(R^(2)) rArr E = (1)/(4 pi epsi_(0)) .(q)/(R^(2)) = (sigma)/(epsi_(0))`
where ` sigma = (q)/( 4 pi R^(2)) ` = surface charge density corresponding to above equation the correct graphs are shown in option (D).