A point charge moves from point
in the field of an opposite electric charge. You can modify the path taken by dragging the locators. At each point of the path, the charge experiences a force
that can be represented by a vector (orange) that makes an angle
with the differential displacement
(blue). Summing the dot product of vectors along the curve (summarized on the right side) gives the total work
performed by the charge. The total work does not depend on the shape of the curve, only on the initial and final points. In this case, work is done only by the radial displacement, the dot product with the tangential component being zero. Work is independent of path only for a conservative field, which includes electrostatic and gravitational fields.