# For a charge to have potential, why bring test positive charge closer to the point charge from infinity in uniform speed? why not variable speed?

For a charge to have potential, why bring test positive charge closer to the point charge from infinity by keeping it in 'electrostatic equilibrium'? or bring the charge closer to the point charge with 'uniform speed'? Why cannot we just bring the charge closer to point charge with variable speeds or acceleration to acquire potential?

• The change in potential will be the same regardless of how the charge is brought in from infinity Commented Dec 10, 2022 at 10:30
• Or I guess I should say, the change in potential energy will be the same, but this is not directly measurable along any given trajectory. The net work done is what defines the potential energy. Commented Dec 10, 2022 at 10:39
• @tparker Potential depends only on position. In order for the change in potential to equal the work done the change in kinetic energy must be zero Commented Dec 10, 2022 at 10:49
• @BobD Yes I agree (I deleted my incorrect first comment), but what I think the OP is getting at is that the potential energy is often defined with respect to paths for which the initial and final speed are the same. Commented Dec 10, 2022 at 10:56
• Conservation of energy then becomes a nontrivial result rather than being true by definition. Commented Dec 10, 2022 at 10:58