Let the electrostatic field $\mathrm{E}$ at distance $\mathrm{r}$ from a point charge $q$ not be an inverse square but, instead an inverse cubic, e.g. $\overrightarrow{\mathrm{E}}=\mathrm{k} \frac{\mathrm{q}}{\mathrm{r}^{3}} \hat{\mathrm{r}}$ Here $\mathrm{k}$ is a constant. Consider the following two statements (i) Flux through a spherical surface enclosing the charge is $\phi=q_{\text {enclosed }} / \in_{0}$ (ii) A charge placed inside uniformly charged shell will experience a force. Choose the correct option.

• A

  Only (i) is valid
• Correct answer
  B

  Only (ii) is valid
• C

  Both (i) and (ii) are invalid
• D

  Both (i) and (ii) are valid

Solution

$|\overrightarrow{\mathrm{E}}|=\frac{\mathrm{kq}}{\mathrm{r}^{3}}$ $\therefore \mathrm{d} \phi=\overrightarrow{\mathrm{E}} \cdot \overrightarrow{\mathrm{dS}}$ $\phi=\int \mathrm{d} \phi=\int \overrightarrow{\mathrm{E}} \overrightarrow{\mathrm{dS}}=\frac{\mathrm{kq}}{\mathrm{r}^{3}} \cdot 4 \pi \mathrm{r}^{2}$ $\phi=\frac{\mathrm{kq} 4 \pi}{\mathrm{r}} \neq \frac{\mathrm{q}_{\mathrm{en}}}{\varepsilon_{0}}$
force on $q^{\prime}$ is zero

Hence, the correct answer is option: 'B'.