question_answer

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

A)  the field is zero but potential is non-zero

B)  potential is zero and the field is infinity

C)  both the field and potential are zero

D)  both the field and potential are non-zero

E)  the field is non-zero but potential is zero

Correct Answer: E

Solution :

 Potential due to charge -q at A \[{{V}_{A}}=\frac{1}{4\pi {{\varepsilon }_{0}}K}\frac{-q}{{{({{r}^{2}})}^{1/2}}}\] Potential due to charge -q at B                 \[{{V}_{B}}=\frac{1}{4\pi {{\varepsilon }_{0}}K}\frac{-q}{{{({{r}^{2}})}^{1/2}}}\] Potential due to charge\[+2q\]at C                 \[{{V}_{C}}=\frac{1}{4\pi {{\varepsilon }_{0}}K}\frac{2q}{{{({{r}^{2}})}^{1/2}}}\] Total potential at centre \[V={{V}_{A}}+{{V}_{B}}+{{V}_{C}}\] \[V=0\] From charge configuration at the centre electric field is non-zero.