Potential and potential energy

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?

• 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. – Steeven Jul 22 '19 at 20:57
• 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. – Puk Jul 22 '19 at 20:58
• @Steeven Maybe the OP is confused about if the charge is negative? – Aaron Stevens Jul 22 '19 at 21:01
• Yes. Charge is negative. – user3728644 Jul 22 '19 at 21:04
• – Aaron Stevens Jul 22 '19 at 21:10

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.