Question

Five equal charges each of value $q$ are placed at the corners of a regular pentagon of side $a$. The electric field at the centre of the pentagon is:

• A. $\frac{q}{4\pi {\epsilon }_0{r}^2}$
• B. $\frac{q^2}{4\pi {\epsilon }_0{r}^2}$
• C. $\frac{2q}{4\pi {\epsilon }_0{r}^2}$
• D. zero

Answer 1

The correct option is D zero

The point $O$, the center of the pentagon is equidistant from all the charges at the end point of pentagon. Thus, due to symmetry, the electric field due to all the charges are cancelled out. As a result electric field at $O$ is zero.