For spherical symmetrical charge distribution, variation of electric potential with distance from centre is given in diagram. Given that:-
$V = \frac{q}{4 π ε_{0} R_{0}}$ for $r R_{0}$ and $V = \frac{q}{4 π ε_{0} r}$ for $r \geq R_{0}$ .
Then which option is incorrect:

Total charge within $2 R_{0}$ is $q$ .
Total electrostatic energy for $r \leq R_{0}$ is zero
At $r = R_{0}$ electric field is discontinuous.
There will be no charge anywhere except at $r = R_{0}$

Question

For spherical symmetrical charge distribution, variation of electric potential with distance from centre is given in diagram. Given that:-
$V = \frac{q}{4 π ε_{0} R_{0}}$ for $r R_{0}$ and $V = \frac{q}{4 π ε_{0} r}$ for $r \geq R_{0}$ .
Then which option is incorrect:

Total charge within $2 R_{0}$ is $q$ .
Total electrostatic energy for $r \leq R_{0}$ is zero
At $r = R_{0}$ electric field is discontinuous.
There will be no charge anywhere except at $r = R_{0}$

Toppr Admin · Accepted Answer

V-q4-x3C0-x3B5-oRo-x2234-cheisqSooptionAiscorrectE-0insider-Ro-KqR2outsider-x2265-Ro-x2234-Eisdiscontinuousofr-RoSooptionCiscorrectalsotherewillbenocheexceptatr-RoSooptionDiscorrect-electrostaticsenergyforr-lt-Roiszerobutifisnotzeroforr-RoSooptionBiswrongHence-optionA-CandDiscorrectanswer-

V=q4πεoRo∴cheisqSooptionAiscorrectE=0insider=Ro=KqR2outsider≥Ro∴Eisdiscontinuousofr=RoSooptionCiscorrectalsotherewillbenocheexceptatr=RoSooptionDiscorrect.electrostaticsenergyforr<Roiszerobutifisnotzeroforr=RoSooptionBiswrongHence,optionA,CandDiscorrectanswer.