## In This post you will get answer of Q.

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 and the electric potential $V (r)$ with the distance $r$ from the centre, is best represented by which graph?

Solution:

## For inside points $(r le R) $

$E = 0, , Rightarrow, , V =constant = frac{1}{4 pivarepsilon_0} frac{q}{R}$

For inside points $(r ge R) $

$hspace18mm E = frac{1}{4 pivarepsilon_0}.frac{q}{r^2}$ or $E propto frac{1}{r^2}$

and $hspace10mm V = frac{1}{4 pivarepsilon_0}frac{q}{r}$ or $V propto frac{1}{r}$

On the surface (r = R)

$hspace20mm V = frac{1}{4 pivarepsilon_0}frac{q}{R}$

$Rightarrowhspace15mm E = frac{1}{4 pivarepsilon_0}.frac{q}{R^2}=frac{sigma}{varepsilon_0}$

where, $ sigma = frac{q}{4 pi R^2}=$ surface charge density corresponding to above equations the correct graphs are shown in option (d).