Question

For spherical symmetrical charge distribution, variation of electric potential with distance from centre is given in diagram. Given that:-
$V=\frac{q}{4\pi {\epsilon }_0{R}_0}$ for $r{R}_0$ and $V=\frac{q}{4\pi {\epsilon }_{0}r}$ for $r\ge R_0$.
Then which option is incorrect:

• A. Total charge within $2R_0$ is $q$.
• B. Total electrostatic energy for $r\le R_0$ is zero
• C. At $r=R_0$ electric field is discontinuous.
• D. There will be no charge anywhere except at $r=R_0$

Answer 1

The correct option is B Total electrostatic energy for $r\le R_0$ is zero

$\begin{array}{c}V=\frac{q}{4\pi {\epsilon }_o{R}_o}\\ \therefore cheisq\\ SooptionAiscorrect\\ E=0insider=R_o\\ =\frac{Kq}{R^2}outsider\ge R_o\\ \therefore Eisdiscontinuousofr=R_o\\ SooptionCiscorrect\\ alsotherewillbenocheexceptatr=R_o\\ SooptionDiscorrect.\\ electrostaticsenergyforr<R_o\\ iszerobutifisnotzeroforr=R_o\\ SooptionBiswrong\\ Hence,\\ optionA,CandDiscorrectanswer.\end{array}$