Question

In a certain region of the space the electric field at a point whose position vector is $\overrightarrow{r}$ is given by $\overrightarrow{E}\left(r\right)=\frac{a}{r}\hat{r},$ where $a=180Nm/C.$ How much electric charge is enclosed inside a sphere of radius $R=0.5m$ centered at origin?

• A. $5nC$
• B. $2.5nC$
• C. $10nC$
• D. $12.5nC$

Answer 1

The correct option is A $5nC$

$E\cdot ds=\frac{q_0}{{\epsilon }_0}$

$\frac{180}{r}\times \pi r^2=q_0$

After substituting the values, we get

$q_0=5nC$