A small test charge q₀ is moved in the field of a fixed point charge Q…

Step 1. The arc. Every point on a circle about $Q$ is at the same distance from $Q$, so $V = kQ/r$ is the same at every point. The potential difference is zero, so the work is zero.

Step 2. Out and back. The field of a fixed charge is conservative. The work depends only on the end points. Going out and coming back to the same point means the same start and end point, so the net work is zero. The straight outward part is positive or negative, and the return path cancels it.

Step 3. The student. The field must be perpendicular to an equipotential line. If it met the line at $60^\circ$, the field would have a part along the line. A charge moving along the line would then gain or lose energy, and the potential would not be constant along it.