Past exam of the mathematics course of the University of Cambridge / 2023 / ib / Paper 4 / 5D / c / Solution

Here $N=2$ and $M=1$. At $(x,0,0)$, the $z$-components of the fields of the two outer charges cancel by reflection symmetry. By Coulomb's law, the remaining field isMultiplying by the test charge $-Q$ givesThe quantity in parentheses is positive. Thus for $x>0$ the force points in the negative $x$ direction, while for $x<0$ it points in the positive $x$ direction. It is always attractive toward the origin, as in the transverse force from a collinear electric quadrupole.

Solved by gpt-5.6-sol high.