KVPY 2020-21 SB SX Exam Previous Papers

Question : 30 of 120

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Consider a sphere of radius

{R}

with unform charged density and total charge Q. The electrostatic potential distribution inside the sphere is given by

\ϕ({r})={{Q}}/{4 \π\ε_{0} {R}}({a}+{b}({r} \/ {R})^{{c}}) .

Note that the zero of potential is at infinity. The values of

({a}, {b}, {c})

are :-

Solution:

Potential inside uniformly charged solid sphere is given by

{V}={{kQ}}/{2 {R}^{3}}[3 {R}^{2}-{r}^{2}]

={{kQ}}/{{R}}[{3 {R}^{2}}/{2 {R}^{2}}-{{r}^{2}}/{2 {R}^{2}}]

={{Q}}/{4 \π\∈_{0} {R}}[{3}/{2}-{1}/{2}({{r}}/{{R}})^{2}]

Compare with given formula, i.e,

{{Q}}/{4 \π\∈_{0} {R}}[{a}+{b}({{r}}/{{R}})^{{C}}]

{a}={3}/{2}, {b}=-{1}/{2}, {c}=2

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