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Why does electric potential definition need to distinct a positive test charge since the result will be the same even with a negative test charge? We could define electric potential with agnostic sign of test charge.
Page 687 from Halliday-Resnick 10 edition: "the electric potential is the amount of electric potential energy per unit charge when a positive test charge is brought in from infinity"
Its not electric potential is defined ss the amount of work done by an external source in moving from infinity to point r away from the source PER UNIT CHARGE. not pet positive charge, you get a positive potential at a point meaning you need to do positive work(per unit charge) to move it to that point if the charge is negative then you do the negative of that work you calculated generally earlier. its just a consequence of positive charged following field lines defined by the definition of our fields. but it doesnt really matter as if you do the math you multiply by the charge which fixes your answer. key point work done by a force in moving from a to b is the negative of amount of work donw by an external source in moving from a to b , so - × integral of f/q . dr from a to b is work i would have to do PER UNIT CHARGE to move from a to b
