Question

In a certain region of space, the electric field is zero. from this fact, what can you conclude about the electric potential in this region?

Answer 1

The answer is that it is constant. The relation between electric field and electric potential is given as, E=  -gradient (V).  The E, the partial rate of change of Electric potential, in the equation implies that the V, the partial differential of the potential of the three-dimensional space (assuming it is considered) is constant.