= Image charges in a sixty-degree conducting wedge
For two grounded conducting half-planes meeting at angle $\pi/3$, place a <point charge> $q$ at radius $d$ on the bisector $\theta=\pi/6$. The <method of images> closes after six copies: positive copies at angles $\pi/6+2k\pi/3$ and negative copies at $-\pi/6+2k\pi/3$, for $k=0,1,2$. Only the first positive copy is real. Opposite-sign reflected pairs make the <electric potential> vanish on both faces; the <uniqueness theorem for the electrostatic potential> proves the construction. Summing the five <image charge> <electric fields> gives the <electrostatic force> $\mathbf F=-q^2(5/4-1/\sqrt3)\widehat{\mathbf e}_r/(4\pi\epsilon_0d^2)$, towards the intersection. The coefficient follows from distances $d$, $\sqrt3d$, and $2d$ to the adjacent negative, nonadjacent positive, and opposite negative copies.
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