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In a dipole case (1 proton / 1 electron), we draw $E$ field lines such as they go and move into the negative charge. If we take an example point near negative charge's upside vertically, we see there that the final $E$ field direction would be downwards to the negative charge. This logic all makes sense if we place positive test charge at that point which would feel the force downward direction. The same logic applies to other points. We use vector addition for both charge's E fields at each point to draw the final E vector.

As pointed out, This works pretty well in case positive test charge is placed at a point(it would directly feel the force in the same direction as the final vector direction), but it stops working if placed negative test charge. If you place electron at the point I marked black, it wouldn't feel the effect to go downwards, but to go upwards/right.

What's the point of drawing such $E$ field lines as below? Is it only handy for positive test charges? It's true that if we wanna know the direction of negative test charge in such field line, it would be the opposite direction of that joined vector for positive test charge. Is it just convention we chose to draw such things for positive test charge?

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It's just the convention. You can blame Benjamin Franklin for it being this way rather than the other way around.

Ultimately, it's a vector quantity, so we need to have an arrow point one way or the other. It's ultimately just arbitrary.

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  • $\begingroup$ It's funny that we got conventions like this due to him. Thanks. $\endgroup$
    – Matt
    Jun 6, 2023 at 23:23

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