Question

For spherical symmetrical charge distribution, variation of electric potential with distance fro center is given in diagram. Given that :$V=\frac{q}{4\pi {\epsilon }_0{R}_0}$ for $r\le R_0$ and $v=\frac{q}{4\pi {\epsilon }_{0}r}$ for $r\ge R_0$
Then which option (s) are correct:

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

Answer 1

Answer: (A), (B), (C)

Total electrostatic energy
for $r\le R_0$ is non-zero
Total charge within $2R_0$ is q
At r=$R_0$ electric field is discontinuous

$V=\frac{q}{4\pi {ϵ}_0{R}_0}$ for $r\le R_0$

$V=\frac{q}{4\pi {ϵ}_{0}r}$ for $r\ge R_0$

Total charge within $2R_{0}nq$. Total electrostatic energy for $r\le R_0$ is non-zero at $r=R_0$ electric field is dis continuous.

Because, total charge always $q$ and electrostatic energy $=0$

$r=R_0$ will be the discontinuous due to heavy potential.