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I know when a negative charge moves in the direction of a uniform electric field its potential energy increases and its potential decreases. For example, its potential energy changes from $0.9\ \rm{mJ}$ to $1.2\ \rm{mJ}$, but its potential changes from $-90\ \rm V$ to $-120\ \rm V$. Where is the potential zero, and where is the potential energy zero? Do they become zero at different locations?

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  • $\begingroup$ I don't think this is correct. The Electric potential associated with a point is just electric potential energy per charge ("volt" is "Joules per coulomb". If one increases, the other would increase as well, and vice versa. $\endgroup$ – Steeven Jul 22 '19 at 20:57
  • $\begingroup$ Usually in electrostatics you define the potential to be the potential energy per unit charge, so with this definition I don't think for a small test charge the potential and the potential energy can simultaneously change the way you describe. They must remain proportional. $\endgroup$ – Puk Jul 22 '19 at 20:58
  • $\begingroup$ @Steeven Maybe the OP is confused about if the charge is negative? $\endgroup$ – Aaron Stevens Jul 22 '19 at 21:01
  • $\begingroup$ Yes. Charge is negative. $\endgroup$ – user3728644 Jul 22 '19 at 21:04
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Electric potential is just the electric potential energy per charge. In other words, electric potential just depends on the charge distribution around you, where as if you were looking at a charge in the field caused by the charge distribution you could then say it has an associated potential energy in that configuration.

In light of this, the relation between electric potential energy $U$ and electric potential $V$ for a charge $q$ is just $$U=qV$$ Therefore, these two values need to be equal to $0$ at the same point in space. Of course, this $0$ point can be chosen to be at various locations, but once you set it then you have to stay consistent, and $U$ and $V$ will both be $0$ at that location.

Therefore your example is totally fine. If the potential energy goes from $0.9\ \rm{mJ}$ to $1.2\ \rm{mJ}$ and your potential goes from $-90\ \rm{V}$ to $-120\ \rm{V}$ nothing is wrong. In either case the values are moving farther away from $0$. If you moved the charge in the other direction back to where one value was $0$, you would find the other value to be $0$ as well.

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  • $\begingroup$ Ok. Then my example is wrong? potential energys in two points are 0.9 and 1.2 and potentials related to two points are 90 and 70.This is wrong? $\endgroup$ – user3728644 Jul 22 '19 at 20:55
  • $\begingroup$ @user3728644 Do you mean because all of your numbers are positive? $\endgroup$ – Aaron Stevens Jul 22 '19 at 20:58
  • $\begingroup$ Suppose potential from left to right decreses. Then potential become zero in right side. But potential energy encreases from left to right then potential energy must become zero in left side. $\endgroup$ – user3728644 Jul 22 '19 at 21:02
  • $\begingroup$ @user3728644 Your example is false because the potential and potential energy do not have the same ratios. You need to think of an example where the charge is kept constant $\endgroup$ – Aaron Stevens Jul 22 '19 at 21:07
  • $\begingroup$ Are these numbers correct? 0. 9 and 1.2 for potential energy and minuse 90 and minuse 120 volt for potential. $\endgroup$ – user3728644 Jul 22 '19 at 21:12

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