Final answer:
The electric potential energy of a particle with charge q is the same at all points on an equipotential surface.
Step-by-step explanation:
True
The electric potential energy of a particle with charge q is the same at all points on an equipotential surface. An equipotential surface is a region in which all points have the same electric potential. This means that the work required to move the particle from one point to another on the equipotential surface is zero.
For example, let's consider a positive point charge surrounded by an imaginary sphere of radius r. The electric potential at any point on the sphere is given by V=kQ/r, which means that the potential is the same at all points on the sphere.