# Why do we use a unit positive charge while calculating the electric potential? Can't we use unit negative charge?

Electric potential is the amount of Work required to move a unit positive charge from infinity to a region of an electric field. Why do we need a positive charge for that? Can't we use negative charge?

• Wikipedia: “A convention is a selection from among two or more alternatives, where the rule or alternative is agreed upon among participants.” Commented May 1, 2023 at 4:08

It is mathematically helpful to treat opposite charges as having the opposite mathematical sign. It allows us to add the charges of an electron and a proton together to get zero, which corresponds helpfully to the charge on a neutral atom.

To make this work we have to decide which of the two types of charge corresponds to positive numbers. It would be too confusing to say that a negative charge corresponds to a positive number, so we say that a positive charge corresponds to a positive number. Hence the unit charge is a positive one.

For the corresponding situation in magnetostatics a positive magnetic "charge" is a North pole. There is no reason South could not have been chosen, but now the choice has been made it is most helpful to stick with it.

The potential at a point is the work required to move a unit test charge from infinity to that point. This means that if you do work $$W$$ and the charge is $$q$$, the potential is $$W/q$$. $$q$$ can be negative, you don't have to use a positive charge.

While it might be helpful to define [potential as "potential energy per unit positive charge"] when introducing the concept, strictly speaking "positive" here is redundant. Charge here can be a positive or negative number (it does not refer to the magnitude of charge), and the sign of the potential energy will naturally change based on that. In fact defining potential as "potential energy per unit positive charge" seems incomplete to me, because it doesn't explicitly prescribe what to do when you have a negative charge, e.g. how to calculate the potential energy of a negative charge from a given potential.

The use of a positive test charge is a convention which, as far as I know, has been agreed by all.
A change to the use of a negative test charge would require an extremely good reason for doing so.
What might that reason be?

An example of where there was a move to completely change a convention which did not succeed was the direction of conventional current, the direction of flow of positive charges.
In 1752 Benjamin Franklin decided that the direction of current flow was in the direction of the flow of positive charges.
However, many years later the role of the electron as the charge carrier was discovered and a debate ensued as to whether or not to change the convention current flow direction from that of positive charge to that of negative charges.

Over time it was decided to use a convention appropriate to the situation, eg circuit network theory tends to use the flow of positive charges but in semiconductor theory the direction of flow of charges is considered.

As long as you know which convention is being used, there should be no problem?