Question

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

Three charges $2q,-q,-q$.

$E\ne 0$

$V=0$

$E=\frac{1}{4\pi {ϵ}_0}\frac{2q}{R^2}$

$E^1=\frac{1}{4\pi {ϵ}_0}\frac{q}{R^2}$

$E^{11}=\frac{1}{4\pi {ϵ}_0}\frac{q}{R^2}$

Now, $E=\frac{1}{4\pi ϵR^2}(2q+q+q)\ne 0$

But $V=\frac{1}{4\pi {ϵ}_{0}R}(2q-q-q)=0$