(Solution) - Three point charges are placed on the y axis a charge -(2025 Original AI-Free Solution)

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Three point charges are placed on the y-axis: a charge q at y = a, a charge - 2q at the origin, and a charge q at y = -a. Such an arrangement is called an electric quadrupole.
(a) Find the magnitude and direction of the elec1ric field at points on the positive x-axis.
(b) Use the binomial expansion to find an approximate expression for the elec1ric field valid for x » a. Contrast this behavior to that of the elec1ric field of a point charge and that of the elec1ric field of a dipole.