Question

If the electric field $\overrightarrow{\mathbf{E}}$ 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 $\overrightarrow{\mathbf{E}}$.

Short answer

If the electric field is uniform in a region, then the electric potential at any point in a uniform magnetic field is also uniform.

If the electric potential is uniform in a region, then the value of the electric field in that region will be zero.

Step-by-step solution

Understanding of electric field and electric potential

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.

Relationship between the electric field and electric potential if the electric field is uniform in a region

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.

Relationship between the electric field and electric potential if the electric potential is uniform in a region

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.