Electric potential — common mistakes

Always pay close attention to the sign of charges when calculating electric potential ($V$) and electric potential energy ($U$). A positive source charge creates positive potential, while a negative one creates negative potential. For potential energy, an attractive force (opposite charges) results in negative potential energy, while a repulsive force (like charges) results in positive potential energy. Incorrect signs are a common mistake!

Electric potential (V) is the work done per unit positive charge to move it from infinity to a point in an electric field. It's a property of a point in space. Electric potential energy (U) is the total work done to bring a specific charge from infinity to that point. It's a property of a charge at a point. So, $U = qV$.

Infinity is chosen as the reference point for zero potential because the electric field and force due to any finite charge configuration effectively become zero at an infinite distance. This makes calculations simpler and provides a consistent baseline for defining absolute potential.

Electric potential can be negative if the source charge creating the field is negative. A positive test charge would be attracted to a negative source charge, meaning the field does work on the test charge as it approaches. This corresponds to a negative change in potential energy, hence a negative potential relative to infinity.

Work done 'on the charge' (by an external force) increases its electric potential energy, so $W_{on} = \Delta U = q\Delta V$. Work done 'by the field' decreases the system's potential energy, so $W_{field} = -\Delta U = -q\Delta V$. They are equal in magnitude but opposite in sign. If a charge moves naturally (e.g., repulsion), the field does positive work. If a charge is moved against its natural tendency, an external force does positive work.