= Solution
For <image charges in a sixty-degree conducting wedge>, use <polar coordinates> in a cross-section normal to the planes' intersection, putting the physical wedge at $0<\theta<\pi/3$ and the real <point charge> at $(r,\theta)=(d,\pi/6)$. Repeated reflection in the two grounded faces produces five <image charges>, all at radius $d$ and the same coordinate along the intersection:
$$
\begin{array}{c|rrrrrr}
\theta&30^\circ&90^\circ&150^\circ&210^\circ&270^\circ&330^\circ\\
\text{charge}&q\ (\text{real})&-q&+q&-q&+q&-q
\end{array}
$$
Equivalently, the positive copies are at $\theta=\pi/6+2k\pi/3$ and the negative copies at $\theta=-\pi/6+2k\pi/3$, for $k=0,1,2$. Only the original <point charge> lies inside the physical wedge.
\Image[/past-exam-of-the-physics-2-paper-of-the-university-of-oxford/2021-wedge-image-charges.png]
{title=Five image charges outside the physical sixty-degree conducting wedge}
For any observation point on either face, reflection pairs every positive <point charge> with an equidistant negative one. Their <Coulomb potentials> cancel, so both grounded faces have zero <electric potential>. The <electric potential> also tends to zero at infinity. The <uniqueness theorem for the electrostatic potential> then identifies this <method of images> construction with the physical solution.
Back to article page
