TRUE. If the electric field is zero everywhere inside a region of space, that means there are no electric field lines or any force acting on a charged particle placed within that region. In other words, the electric potential energy experienced by a charged particle in that region is constant, regardless of its position. Since the potential difference between two points is defined as the work done to move a unit positive charge between those two points, a constant potential difference implies zero potential difference. Therefore, the potential is zero throughout that region.
