Question

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

Answer 1

Answer: (E)

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.