Three point charges are affixed at the vertices of an isosceles triangle in the…
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
Three point charges are affixed at the vertices of an isosceles triangle in the xy-plane as follows:
• +2.0μC at A(−0.10m,0)
• +2.0μC at B(+0.10m,0)
• −3.0μC at C(0,0.16m)
Assume the potential at infinity is zero.
(a) Derive a symbolic expression for the electric potential V(y) at an arbitrary point on the line x=0 (the symmetry axis of the triangle).
(b) Set up the equation whose solution gives the point(s) on x=0 where the electric potential is zero. Show all algebraic steps that reduce the condition V(y)=0 to a solvable polynomial equation.
(c) Solve the equation obtained in part (b) for y. Provide numerical values, indicating which solution(s) lie between the charges and which lie outside the triangle.
(d) Discuss the physical plausibility of each solution, commenting on whether the presence of like charges at A and B limits the number of physically meaningful zero-potential locations along x=0. Support your discussion with qualitative reasoning.