Past exam of the physics 2 paper of the University of Oxford / 2013 resit / 7 / ii

With $q_2=-q_1$, both field contributions between the charges point the same way. Their signed force on $q_3$ isSince $f$ is dimensionless, the small-displacement expansion is $|f|\ll 1$, givingThe force at the midpoint is nonzero and the first variation is quadratic, not linear. In particular, the midpoint is not an equilibrium supporting a linear restoring-force approximation. The printed comparison of $f$ with $L$ is dimensionally inconsistent; the expansion above keeps their distinct roles.