Is potential difference the difference (by mean of mathematical decrement; Y-X
) by decremeting one measured average Joule of a charge (in point B in space) from another measured averaged Joule of a charge (in point A in space)?
Answer
It's correct that the potential is proportional to the potential energy a charged particle might have if it were hypothetically moved to some point in space. And that a potential difference is the difference between the potential at two points.
But practically we can't measure the (electrostatic potential) energy of a charge. In fact this energy has an arbitrary constant offset, depending what point we choose as the reference for zero potential. Also remember that the potential can be defined at a point in space, even if there's no charge there to experience it
But potential difference has another definition, in terms of electric field,
$$V_{ab}=-\int_b^a \vec{E}\cdot d\vec\ell$$
and we can effectively measure potential difference according to this definition.
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