Final answer:
The statement that electrostatic potential is the same at all points on a circle formed by a uniformly charged line is false, because the potential actually varies unless the circle is in a plane perpendicular to the charged line and equidistant from it.
Step-by-step explanation:
The statement that the electrostatic potential at different points on a circle formed by a uniformly charged line will be the same is false. In physics, especially when dealing with electrostatics, the concept of equipotential surfaces is important. Equipotential surfaces are surfaces over which the electric potential is constant.
For a single isolated point charge, the equipotential surfaces are spherical and concentric around the charge, and the potential is given by V = kQ/r, where V is the electric potential, k is Coulomb's constant, Q is the charge, and r is the radius from the charge to the point on the equipotential surface. That being said, the electric potential due to a uniformly charged line (or ring) would indeed be the same along a circle that is in the plane perpendicular to the line and whose center coincides with the center of the line (or ring), as long as we are considering points at an equal distance from the line. However, if considering a circle around the line in the same plane as the line, the distances to different points on the circle would vary, and thus, the electric potential would also vary.