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Electric multipole expansion

Multipole expansion of three collinear charges

For charges $-Q,2Q,-Q$ at $z=d,0,-d$, the exact force on a charge $-Q$ at $(x,0,0)$ is
$$
F=-\frac{Q^2x}{2\pi\epsilon_0}
\left(\frac1{|x|^3}-\frac1{(x^2+d^2)^{3/2}}\right)\widehat x.
$$
It points toward the origin for every nonzero $x$.


Transverse force from a collinear electric quadrupole

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

Transverse force from a collinear electric quadrupole

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Transverse force from a collinear electric quadrupole

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