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