Foundations — Understand conventional current vs electron flow direction

This page assumes you have seen nothing. Before you can understand conventional current vs electron flow, we build every piece of notation the parent note quietly leans on — one at a time, each anchored to a picture.

0. The mental picture we keep returning to

Everything below happens inside a wire: a thin metal tube packed with tiny charged particles. We watch a single flat slice through the wire (a "cross-section") and count what crosses it. Hold that image.

The slice is the imaginary window. Current is the rate stuff crosses this window. Keep looking at the red slice — every symbol below is measured at that slice.

1. Charge — the symbol $Q$ (and $q$)

The picture: think of charge like a colored dot on a particle. Two things carry it:

• Electrons — real particles with negative charge.
• Protons (and, in ideas, "positive carriers") — positive charge.

Why the topic needs it: the whole conventional-vs-electron argument is about the sign of the charge that moves. Without a symbol for "how much charge" ($Q$) and "charge per particle" ($q$), we cannot say why negative movers make the arrow flip. See Electric Charge and the Coulomb for where the coulomb comes from.

2. The elementary charge — the symbol $e$

The picture: imagine charge only comes in identical coins. $e$ is the value of one coin. You can have 1 coin, 5 coins, a trillion coins — but never half a coin.

Sign convention that trips everyone up:

• $e$ itself is always positive (it's just a size).
• An electron's charge is $q=-e$ (negative).
• A proton's charge is $q=+e$.

Why the topic needs it: the parent note computes $q\vec{v}=(-e)\vec{v}$. That $-e$ is the origin of the direction flip. See Semiconductors and Holes for where a positive mobile carrier genuinely exists.

3. Number of carriers — the symbol $N$

The picture: stand at the red slice and tally each electron that passes: 1, 2, 3, … up to $N$.

Putting 2 + 3 together — total charge: $Q=N\times |q|=Ne$ "Total charge = how many carriers $\times$ the charge on each." This is exactly the step in the parent's Example 2, where $N=6.24\times 10^{18}$ electrons gave $Q\approx 1\text{C}$.

4. "Change in" — the symbol $\Delta$

The picture: two snapshots. At the start, some amount has crossed. A moment later, more has crossed. $\Delta Q$ is the difference — the extra charge that went through in between.

Why the topic needs it: current is a rate, and a rate always compares an amount to the time it took. $\Delta$ is the notation for "amount collected over this interval."

5. Time — the symbol $t$, and the second

The picture: a stopwatch running while you count electrons crossing the slice.

Why the topic needs it: current is per second. Without time, "a coulomb crossed" is meaningless — we must know how fast.

6. Current — the symbol $I$, and the ampere

Now we can assemble the parent's central formula.

Reading it piece by piece:

• $\Delta Q$ (top) — how much charge crossed (from §1, §4).
• $\Delta t$ (bottom) — over how long (from §4, §5).
• The fraction bar — "divide," i.e. "per." So $I$ is charge per second.

The picture: a wide, busy slice (lots of charge per second) = big $I$. A trickle = small $I$.

Why $I$ has no sign of its own: notice this formula never mentions whether the carriers are positive or negative. It only counts how much per second. That is precisely why direction is a separate labeling choice — the topic's whole point. See Current and the Ampere.

7. Vectors and velocity — the symbols $\vec{v}$ and $\vec{J}$

The parent jumps to $\vec{J}\propto q\vec{v}$. Two new pieces of notation live there.

The picture: $\vec{v}$ is literally an arrow drawn in space — its length is how fast, its heading is which way.

Why the topic needs vectors: "which way" is a direction, and directions need arrows. Scalars ($I$, $Q$, $t$) can't point.

8. The sign flip — assembling $q\vec{v}=e(-\vec{v})$

Now every symbol is defined, so the parent's key line reads cleanly:

The picture: electrons crawl left; the conventional-current arrow $\vec{J}$ points right. Same physical current, two opposite arrows.

That is the entire foundation for conventional current vs electron flow. The battery terminals ($+$ and $-$) and the push behind the flow come from Voltage and EMF; the equations that then use $I$ come from Ohm's Law.

Prerequisite map

Equipment checklist

Self-test: can you answer each before revealing?