12.2.1 Why EPE can be Positive and Negative

Just like GPE is stored in the gravitational field when two masses are near each other, EPE (electric potential energy) is stored in the electric field when two charges come closer together. And just like GPE, we have chosen EPE’s reference point to be zero (when charges are) at infinite distance apart.

Positive EPE

Imagine two like charges held at some distance apart. When they are released, the repulsive electrical forces will make them accelerate away from each other. So as they move further apart, they are losing EPE in exchange for KE. Isn’t it obvious then that EPE is lower when they are further apart? The furthest they can be from each other is “infinite distance”, where EPE is chosen to be zero. So zero is the lowest EPE for two like charges. Anything nearer than “infinite distance” is positive EPE. The closer the charges, the more positive the EPE.

Negative EPE

Now imagine two unlike charges held at some distance apart. When they are released, the attractive electrical forces will make them accelerate towards each other. So as they move closer together, they are losing EPE in exchange for KE. Isn’t it obvious then that EPE is higher when they are further apart? The furthest they can be from each other is “infinite distance”, where EPE is chosen to be zero. So zero is the highest EPE for two unlike charges. Anything nearer than “infinite distance” is negative EPE. The closer the charges, the more negative the EPE.