Question

Let the electrostatic field E at distance r from a point charge q not be an inverse square but, instead an inverse cubic, e.g., $\overrightarrow{E}=k\frac{q}{r^3}\hat{r}$. Here k is a constant. Consider the following two statements.
(i) Flux through a spherical surface enclosing the charge is $\Phi =q_{enclosed}/{ϵ}_0$
(ii) A charge placed inside uniformly charged shell will experience a force.
Choose the correct option.

• A. Only (i) is valid
• B. Only (ii) is valid
• C. Both (i) and (ii) are invalid
• D. Both (i) and (ii) are valid

Answer 1

The correct option is B Only (ii) is valid

Flux enclosed is not constant since $\int E.ds$ over a surface of radius r is not constant and is inversely proportional to r. hence (i) is not valid.

Also $F=Eq$, initially distance $r$ is inverse square in electric field but now distance r is changed to inverse cube in electric field. hence electric field is changed from initial condition, hence a charge will experience a force. hence (ii) is valid.