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).
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).