ELECTROMAGNETISM & RELATIVITY - Chapter 1, Exercise 3 Solution
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Conceptual: Was Franklin's Convention Really "Wrong"?

PROBLEM
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Explain, in your own words, why calling Benjamin Franklin's
positive/negative naming convention a "wrong guess" is a real
oversimplification - what genuinely IS backwards (relative to real
electron flow), and what is NOT actually a problem for how circuits
are calculated using the conventional-current convention today.

SOLUTION
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What IS genuinely backwards:

Franklin, working in the 1740s, arbitrarily labeled one kind of
electricity "positive" and the other "negative," decades before
anyone knew electrons existed or which particles actually move
through a wire. Once electrons were discovered and identified as the
real charge carriers in a metal wire, it turned out that electrons
(which we now call "negative") flow in the OPPOSITE direction to
what is today called "conventional current" (defined, by Franklin's
own old convention, as the direction positive charge would flow). So
yes, in a real, literal sense, the direction actual electrons move is
opposite to the direction "conventional current" is defined to flow.

What is NOT actually a problem:

Despite this mismatch, conventional current is not "wrong" in any
way that affects circuit calculations. The chapter's own text states
the key physical fact directly: a flow of positive charge in one
direction produces exactly the same measurable electrical effect (the
same current, the same voltage drops, the same power delivered) as an
equal flow of negative charge in the opposite direction. Every
circuit law, every calculation using conventional current, gives
correct, verified real-world answers - the convention is internally
self-consistent and simply describes an equivalent, equally valid way
of accounting for the same physical current.

ANSWER: What's genuinely backwards is the DIRECTION LABEL: real
electrons move opposite to the direction "conventional current" is
defined to flow. What's NOT a problem is that this mismatch has zero
effect on the correctness of circuit calculations, since a flow of
positive charge one way is physically indistinguishable, in every
measurable respect, from a flow of negative charge the other way.
Calling this a "wrong guess" implies Franklin's convention produces
incorrect results, which it does not - it is simply a naming
convention that happened not to match, decades later, which specific
particle turned out to be the one actually in motion.

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WHY THIS WORKS AS AN ANSWER

This distinguishes between two genuinely different claims that are
often conflated in the popular telling: a convention being
"unintuitive" or "coincidentally mismatched with later discoveries"
is a completely different thing from a convention being "incorrect."
Franklin's positive/negative labels remain arbitrary but functionally
sound - exactly the same distinction the chapter draws when it calls
his choice "arbitrary" rather than "mistaken," continuing this
course's own inherited discipline (from Classical Mechanics &
Thermodynamics) of correcting popular oversimplifications with the
real, more nuanced history.