If the electric field \({\bf{\vec E}}\) is uniform in a region, what can you infer about the electric potential V? If V is uniform in a region of space, what can you infer about \({\bf{\vec E}}\).

The region around a charge until where its influence is observed is called the electric field of that charge.

The work done in conducting a tiny charge from infinity to a point within the electric field is called the potential at that point in that field.

For a uniform electric field, the intensity of the electric field is the same at all points in the field, so the work done in bringing a point charge from infinity to any point in the electric field is the same. It means the electric potential at any point in a uniform electric field is the same.

The electric potential is the same in the electric field implies that potential is constant. As the electric field is proportional to the change in potential, the constant potential difference implies zero electric field strength.