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When we place a positive test charge near a positive charge, it moves away from it. If there is a negative one instead, it follows a curved path. That is, the field of positive charges originates from $+$ and terminates in $-$ ones.

If we place a negative test charge then it will move away from a negative charge and towards a positive one.

So we say the electric field originates from the negative charge and ends in the positive one. It really depends on the test charge.

Why do we only take positive test charges to find the field direction?

Why are we told that the field originates from positive charges and ends in negative ones?

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It is strictly a matter of convention that the direction of the electric field is the direction of the force that a positive charge would experience if placed in the field. It could just as well have been the other way around.

Hope this helps

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At the time when the notation of the plus and minus pole was introduced, the nature of electric current was unknown. Something flows and of course the notation was from "+" (a lot of something) to "-" (less of something).

Franklin proposed that "vitreous" and "resinous" electricity were not different types of "electrical fluid" (as electricity was called then), but the same "fluid" under different pressures.… Franklin was the first to label them as positive and negative respectively,

In a translation from the German Wikipedia, it sounds like this:

The term "technical current direction" is primarily historically conditioned; it assumes a flow of charges that move - following the field line direction of the electric field - from the positive to the negative voltage pole. The fact that it is the electrons in metallic conductors, on the other hand, that cause the current flow as charge carriers and thereby flow exactly the other way round from the negative to the positive pole, was still unknown at the time of this conceptualisation.

Too long, don't read.
I would like to contradict the last sentence a little. There would be no confusion if the electron had been assigned the sign "+". It is pure convention to designate protons with "-" and electrons with "+" the other way round.
I could not find a source as to who and when labelled the electron with the minus sign. But that was the really wrong decision because the electric current in our daily life consists of moving electrons and to label the current as flowing from plus to minus is very intuitive.

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