the direction of electrical field in Colomb's formalism is an experimental work? can we detect the direction theoretically?

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I am absolutely sure we can. At the moment a friend of mine has a course on that. But I don't know exactly how to do it. It somehow works with the electrostatic potential. \[ \vec{E} = -\vec{\nabla}\phi\] Than the electrical field is the way a free electron would take. And the electrical field is orthogonal to equipotential. I hope that'll give you an Idea on how to solve the problem.

may be! I have to think and then continue this discussion! thanks Kathi!

it is just a definition. You just have to define it once and then stick to that definition, otherwise your theories become inconstant. After all, there is no "plus" or "minus" in nature, only two opposite charges that we needed a name for...

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