Question

Two equal charges $q$ each are placed at the two vertices of an equilateral triangle of side $r$. The magnitude of electric field intensity at the third 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)

$\frac{\sqrt{3}q}{4\pi {\epsilon }_0{r}^2}$

Due to charge at A and B magnitude of intensity of electric field at point $C$

$E_1=E_2=\frac{1}{4\pi {\epsilon }_0}.\frac{q}{r^2}$

Net intensity at point C is

$E_R=\sqrt{E_1^2+E_2^2+2E_1{E}_{2}cos{60}^o}$

$=\sqrt{E_1^2+E_1^2+2E_1^2\times \frac{1}{2}}=\sqrt{3}{E}_1=\frac{\sqrt{3}q}{4\pi {\epsilon }_0{r}^2}$