# Why electric potential at each point in a uniform electric field is not same?

why potential at any point in a uniform electric field is not same i.e. why potential difference between any two points in the uniform electric field is not zero? According to me if i bring a test charge from infinity to a point A in uniform electric field [assume the field is due to a positive charge] then i will have to apply external force on the test charge against the electrostatic force by the uniform field such that external force is equal to electrostatic force so that kinetic energy of test charge would remain constant thus some potential energy will be stored in the test charge at point A.....NOW if i will bring the test charge from infinity to some another point in the uniform electric field...let the point be B then according to me i will do the same amount of work done on the test charge to bring it to point B because i will apply the external force that will also be equal to electrostatic force by the uniform electric field.....and because the electric field is uniform the test charge will experience the same amount of electrostatic force at each point on the uniform electric field i.e. electrostatic force at both the points A and B due the field will be same. Hence according to me the potential energy at each point on the uniform electric field will be the same thus the potential also. Kindly explain.... why not? thanks!

• 1) don't start at infinity, since everything is infinite. 2) Consider a mass in uniform gravitational field for better intuition.
– JEB
May 28 at 15:00
• @JEB Thanks💫 but this didn't gave my answer...can you pls explain a bit more...i will be very grateful 😊 May 28 at 15:07
• Because potential is not a function of one point, that is a 3-variable function such as $\phi = f(x,y,z)$, but rather potential is a function of two points, that is a 6-variable function such as $\psi = f(x_1,y_1,z_1, x_2, y_2, z_2)$ May 28 at 15:35
• Thanks💫....... May 28 at 16:01