Question

Equal charges $q$ each are placed at the vertices of an equilateral triangle of side $r$. The magnitude of electric field intensity at any vertex is

• A. $\frac{2q}{4\pi {\epsilon }_0{r}^2}$
• B. $\frac{q}{4\pi {\epsilon }_0{r}^2}$
• C. $\frac{\sqrt{3}q}{4\pi {\epsilon }_0{r}^2}$
• D. $\frac{\sqrt{2}q}{4\pi {\epsilon }_0{r}^2}$

Answer 1

Answer: (C)

The magmitude of intensity of electric field at point
$C$ due to charge at $A$ and $B$ is
$E_1=E_2=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q}{I^2}$

So, the net intensity at point $C$ is
$E_R=\sqrt{E_1^2+E_2^2+2E_1{E}_2\cos 60^{\circ }}$
$=\sqrt{E_1^2+E_1^2+2E_1^2\times \frac{1}{2}}=\sqrt{3}$
$\therefore E_1=\frac{\sqrt{3}q}{4\pi {\epsilon }_0{r}^2}$