Question

Three charges $2q$, $-q$ and $-q$ are located at the vertices of an equilateral triangle. At the center of the triangle,

• A. the field is zero but potential is non-zero
• B. the field is non-zero but potential is zero
• C. both field and potential are zero
• D. both field and potential are non-zero

Answer 1

The correct option is B the field is non-zero but potential is zero


$\Delta ABD$ is the equilateral triangle, and $\text{C}$ is the centre of the triangle.

So $CA=CB=CD=r$

Potential at the centre of triangle will be

$V_c=V_{2q}+V_{-q}+V_{-q}$

$\Rightarrow V_c=\frac{k2q}{r}-\frac{kq}{r}-\frac{kq}{r}=0$

And for $E_c$ we need to add the electric field vectors due to charges $2q,-q,-q$

$\overrightarrow{E_c}={\overrightarrow{E}}_{2q}+{\overrightarrow{E}}_{-q}+{\overrightarrow{E}}_{-q}$


From the above diagram we can clearly see that the $\text{x}$ component of net field will be zero. But there will be a non-zero $y$ component of the net field.

Hence, option $\left(b\right)$ is the correct answer.