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.

 

[sardar]

The choice of using proton test charges instead of electron test charges for electric fields is based on historical convention and practicality.

Historically, the concept of electric fields was first introduced by physicist Michael Faraday in the 19th century. At that time, the existence of electrons was not yet known and the concept of positive and negative charges was not fully understood. Therefore, Faraday and other scientists at the time used positive test charges to study electric fields.

Additionally, it is more practical to use proton test charges instead of electron test charges for electric fields. Protons have a much larger mass than electrons and are therefore easier to manipulate and measure in experiments. This makes it more convenient for scientists to use protons as test charges when studying electric fields.

Furthermore, the use of proton test charges does not affect the understanding of electric fields. The direction of the electric field lines and the strength of the field are still accurately represented, regardless of whether a positive or negative test charge is used.

In terms of potential difference and electrical currents, the focus on electrons is due to their mobility and role in electricity flow. However, this does not negate the use of proton test charges in understanding electric fields.

In conclusion, the use of proton test charges for electric fields is a convention that has been established and proven to be practical. While the focus may shift to electrons in other aspects of electricity, the use of proton test charges for electric fields remains a valid and effective approach.