question_answer

Three charges \[2q,\,-q,\,-q\] are located at the vertices of an equilateral triangle. At the centre of the triangle [MP PET 1985; J & K CET 2004]

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

Correct Answer: B

Solution :

             Obviously, from charge configuration, at the centre electric field is non-zero. Potential at the centre due to 2q charge \[{{V}_{2q}}=\frac{2q}{r}\] and potential due to ? q charge \[{{V}_{-q}}=-\frac{q}{r}\]  (r = distance of centre point) \ Total potential \[V={{V}_{2q}}+{{V}_{-q}}+{{V}_{-q}}=0\]