Why proton test charges and not electrons?

[AKBrown]

When picturing electric fields, they are always based on a positive test charge. As you move on to potential difference and electrical currents, it is based more on electrons/negative charge. So, why aren't electric fields and fields lines based on a negative test charge instead of a positive test charge?

Thank you for your help!

 

[vanhees71]

This is just historical. For some reason one has defined what's now known to be carried by protons as the positive charge. There is a lot of confusion in the literature, talking about "technical direction of current" vs. "real direction of current" and similar gibberish.

It's way easier to just use the vector-field concept to understand these issues. The best is to use even relativistic four-dimensional notation right away. E.g., the electric four-current of a fluid with number density $n_0$ of charge carriers is given by

$$j^{\mu}=q n_0 u^{\mu}=q n_0 \gamma \begin{pmatrix}c \\ \vec{v} \end{pmatrix}, \quad \gamma=\frac{1}{\sqrt{1-\vec{v}^2/c^2}}.$$

Here, $q$ is the charge of one particle ($+e >0$ for protons, $-e<0$ for electrons), $c$ the speed of light, $n_0$ the density of the fluid as measured in the local rest frame of the fluid cell, and $\vec{v}$ the flow-velocity field.

The sign of the total current through a cross section then is uniquely defined by the spatial components of this current-density vector and the orientation of the cross-sectional area:

$$I=\int_{A} \mathrm{d}^2 \vec{A} \cdot \vec{j}.$$

 

[NascentOxygen]

They originally thought that electricity in wires was a flow of positive charges. I guess everything else derives from that erroneous conclusion.

 

[chrisbaird]

Positive charges can also flow and create currents, for instance in solutions, in your body, in the ionosphere. Even in semiconductors, positive charges (holes) can flow and create currents. Just because electrons are the ones moving in metals and humans like to make useful electronic devices out of metals does not make the electrons special when in comes to electrical currents.