This is not a homework, but a question formed in my mind after reading my textbook. 1. The problem statement, all variables and given/known data Consider an electron (a charged particle) on a metallic equipotential surface. We know that all the points on the surface are equipotential, thus there will be no force on charged particles on the surface and no tendancy to move on their own. We move the electron form point i to point f with our applied force. Find the equation for the work on the electron from the applied force. 2. Relevant equations We know from the equation (I) in the attached picture that the work done by the field will be zero because the field lines are prependicular to the surface, thus making the dot product zero. 3. The attempt at a solution From the equations (II) and (III) we see that the work by the applied force is equal to the changes in the electron's kinetic energy, right? But will our work be zero if ΔK=0? Why? Does it cancel with the work from friction? How?