I am casually working through Introduction to Electrodynamics, 3rd ed. by David J. Griffiths and created some theoretical situations to test my understanding of the subject matter. I am having difficulty with some, and will appreciate input. Consider the following theoretical cycle (see the attached figure): A positively charged mass starts from state 1 and falls under the influence of gravity through a horizontally orientated electrical field. Since the acceleration can be broken up into independent orthogonal vectors, the acceleration due to gravity and the acceleration due to the force on the charged mass due to the electric field can be considered independently. The path A the particle is to follow between states 1 and 2 is subject to vertical as well as horizontal acceleration. Upon reaching state 2, the positively charged mass exits the horizontally directed electrical field. Since the mass is no longer subject to a horizontal force, horizontal acceleration will cease and the path B the mass follows to state 3 is subject to vertical acceleration only. (I assume it is this point that causes me to err, see the question below.) At state 3 there is a theoretical transducer that can convert the total kinetic energy of the mass into another form for later use. The mass is moved from state 3 to state 4 in a way that requires no work input (frictionless surface, and all work required to accelerate the mass to get it moving is recovered when it is decelerated to a standstill at state 4, for example). Next, the mass is moved up against the force of gravity to state 5, its initial height. The work required to do this can be considered to be equal to the vertical component of the kinetic energy only that was collected at state 3, for this theoretical reversible lifting process. Path E between states 5 and 1 can be considered to be without work, same as path C. It appears that, if all the assumptions are valid, the horizontal component of kinetic energy collected at state 3 is excess. This is not supposed to happen, and I would appreciate input as to where there is a mistake. Here are some of my assumptions I am suspicious of, as well as possible workarounds: The charged mass exiting the electrical field is subject to some attraction force to the negatively charged plate. This will cause it to experience a force in the vertical direction upon exiting the horizontally directed electrical field. With luck, this force will be exactly equal to the horizontal kinetic energy of the mass after leaving the electric field. This may possibly be overcome by letting the whole falling procedure finish closer to the positively charged plate than the negatively charged one. It may perhaps help to complete paths B and C inside a Faraday cage. The field lines cannot be assumed to be completely horizontal near the edges, due to fringe effects. There is an accompanying magnetic field due to the moving charge that will cause it to have a back magnetic motive force on some sort, and the error arises by analysing an electrodynamic system with electrostatic arguments. This may be overcome by letting the charge complete its path at a constant slow speed inside the electric field, gradually collecting energy from the forced doing work instead of collecting it all at once at state 3. I will appreciate comments as to what I miss from an electrodynamic perspective. The theoretical system appears to gain due to the fact that it can move the positively charged mass to its original horizontal position without doing work against the force that caused it to move to the right, as the restoration movement occurs outside the “force field”.