Presume you are asked to find the electric field at point P whose coordinates are (L, y) for the case of a consistent line segment of charge which extends from x=0 to x=L on the x axis of a Cartesian coordinate system. One should integrate Coulombs law for the electric field at point P due to every charge dq on the line segment. In a denominator of the integrand is a square of a distance written as r2 in Coulomb's Law. In Coulombs law for the electric field because of a point charge the distance in question is the distance from the point charge to the point in space at which the electric field is being computed. What distance do we utilize for the distance in question in the integrand?

Answer:

The integral is the total of the contributions to the electric field at point P because of each infinitesimal bit of charge on the line segment. The distance in question is different for every bit of charge. For every infinitesimal bit of charge the distance in question is the distance from the infinitesimal bit of charge to point P.

The subsequent (incomplete, looping) image shows how the distance in question (labelled r in the diagram) varies with the position of the infinitesimal bit of charge whose contribution to the electric field is under consideration.