# Why is a net flow of positive charge in one direction equivalent to a net flow of negative charge in the opposite direction?

If I understand correctly, conventional current was defined with reference to positive charges because it was found that a negative charge flowing in one direction is actually equivalent to the same amount of positive charge going in the other direction.

Is there any basis for this equivalence?

• Because all that matters in most cases is charge difference. – Steeven Apr 29 at 6:29

## 3 Answers

is there any basis for this equivalence ?

Consider an initially electrically neutral region (equal number of unit positive and negative electric charge) and consider the flow of electric charge through a closed surface enclosing the volume.

Stipulate there is a net outward flow of positive (negative) charge through the surface and see that the region becomes progressively more negatively (positively) charged.

Now, stipulate that there is a net inward flow of negative (positive) charge through the surface and see that the region become progressively more negatively (positively) charged.

That is, the region is becoming progressively more negatively (positively) charged in either case.

• I agree with your answer regarding the equivalence. Just think the OP shouldn't necessarily be left with the impression that the equivalence is the historical basis of the definition of conventional current, i.e., the flow of positive charge. If we can cite an authoritative source that this is in fact the case, I think it completes your answer. I have not been able to find such a source. One that I found is the link to the NASA website. – Bob D Apr 29 at 22:33
• @BobD, I'm not sure I follow. AFAIK, the definition of conventional current isn't "the flow of positive charge". To be sure, a flow of negative charge 'to the left' is (and not equivalent to) an electric current to the right. Electric current is the flow of charge regardless of the polarity of the charge. By convention, the direction of electric current is the same as the direction of positive charge flow and opposite that of negative charge flow. – Alfred Centauri Apr 30 at 0:24
• Yes I understand that it is only by convention that the direction of current is the direction of positive charge and opposite that of negative charge. My only point is that the history of the convention was not because "it was found that a negative charge flowing in one direction is actually equivalent to the same amount of positive charge going in the other direction". Can you cite an historical reference? The only one I could find was the link I gave. BTW I remember my physics profs scoffing at the convention used by electrical engineers, whether justified or not. – Bob D Apr 30 at 11:56
• @BobD, to be clear, I'm intentionally not addressing in any way the historical aspect of the convention. The title of the OP's post asks why a flow of one sign of charge in a direction is equivalent to the flow of the opposite sign of charge in the other direction. By quoting the OP, I hoped to indicate the scope of my answer is limited to the equivalence aspect. – Alfred Centauri Apr 30 at 13:13

It’s an historical question. It is my understanding that the convention for current flow being that of positive charge occurred before electrical current was really understood. So in electrical engineering it’s the convention that stuck. Physicists don’t care for it since we now know that most current is the flow of negative charge, electrons (semi conductor currently being one exception). Bottom line: It doesn’t matter as long as we’re consistent.

UPDATE:

Read that Ben Franklin in static electricity experiments knew there were two types of charge depending on what materials you rubbed together. He thought of current as a fluid which if built up too much , became too “positive”, it would discharge causing a spark.

If this true, then it has nothing to with positive charge going in one direction being equivalent to negative charge going in the opposite direction.

Hope this helps

P.s the above is from “The Direction Assigned to Electric Currents” NASA website Here is the link.https://www-spof.gsfc.nasa.gov/Education/woppos.html

• Bob, after writing a response to your comment to my answer and then revisiting this answer, I do think our understandings of the concept of conventional current are different. My understanding is essentially the same as this quote from the Wikipedia article Electric current: (cont...) – Alfred Centauri Apr 30 at 0:38
• ... "A flow of positive charges gives the same electric current, and has the same effect in a circuit, as an equal flow of negative charges in the opposite direction. Since current can be the flow of either positive or negative charges, or both, a convention is needed for the direction of current that is independent of the type of charge carriers. The direction of conventional current is arbitrarily defined as the same direction as positive charges flow." – Alfred Centauri Apr 30 at 0:38

It's appropriate to remark that equivalence is not always true. I wish to remind you of Hall effect. Shortly said, there is a difference when a conductor is placed in a magnetic field. A weak transverse (wrt current and field) potential difference is observed, and its direction depends on whether charge carriers are positive or negative.

Of course that effect was discovered much later than the sign convention had been established. Initially it was a mistery: some conductors exhibited a sign of Hall effect opposite to the vast majority. Explanation had to wait quantum mechanics and the band theory of solid state.

• It depends what you mean by 'equivalent'. Arguably the flow of positive charge in one direction can be equivalent to the flow of negative charge in the opposite direction without the two sorts of flow being indistinguishable! – Philip Wood Apr 29 at 14:36
• @PhilipWood Surely it's a matter of definition, but... What's your definition of equivalent in present case? If two charge flows are distinguishable how can you call them equivalent? – Elio Fabri May 1 at 7:29
• "What's your definition of equivalent in present case?" Something like: resulting in the same change in charge distribution in the absence of other forces such as magnetic Lorentz forces. Admittedly the caveat considerably weakens the notion of equivalence, which is why I said "arguably". – Philip Wood May 1 at 8:18