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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!

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  • $\begingroup$ 1) don't start at infinity, since everything is infinite. 2) Consider a mass in uniform gravitational field for better intuition. $\endgroup$
    – JEB
    Commented May 28, 2023 at 15:00
  • $\begingroup$ @JEB Thanks💫 but this didn't gave my answer...can you pls explain a bit more...i will be very grateful 😊 $\endgroup$ Commented May 28, 2023 at 15:07
  • $\begingroup$ 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 $\psi = f(x_1,y_1,z_1, x_2, y_2, z_2)$ $\endgroup$
    – hyportnex
    Commented May 28, 2023 at 15:35
  • $\begingroup$ Thanks💫....... $\endgroup$ Commented May 28, 2023 at 16:01

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if pt a and b are at equal distance from the charge brought from infinity both points will have the same potential..... as we know dV/dr= E hence it only depends on the distance bw test charge and the other charge.

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  • $\begingroup$ Even potential or field is not defined on the point itself which is too part of the coordinate plane $\endgroup$
    – agbuddy
    Commented May 28, 2023 at 15:12
  • $\begingroup$ I know that but we have derived KQ/r from the theory that if we bring the charge from infinity to a certain point then the total work done per unti charge is the potential at that point and to find the total work done we needed to integrate....so i just wanted my answer according to this theory that if we bring the test charge from infinity to two different points in the uniform electric field then the potential at both the points should be same since the external force is done against the electrostatic force which is same at both the points because the field is uniform. Thanks💫 $\endgroup$ Commented May 28, 2023 at 15:15
  • $\begingroup$ I would be grateful if you explain me from that point which I have written you in the comment above. $\endgroup$ Commented May 28, 2023 at 15:17
  • $\begingroup$ V(a)=-∫E.dl (limits are infinity to a) similarly V(b)=-∫E.dl (limits are infinity to b) .............so according to you potential differece bw them should be zero.....? $\endgroup$
    – agbuddy
    Commented May 28, 2023 at 15:30
  • $\begingroup$ thanks i got the point now....and i even got that work done will also be different for the different points since magnitude of displacement will be different although the external force would be same.....thank you very much💫 Let me know if I am wrong! $\endgroup$ Commented May 28, 2023 at 15:58

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