Charges act forces on each other. These forces are usually described by electric fields. I don't like that approach.

A better way to think about electric forces is in terms of energy. It takes energy to separate charges. A particle moving from one charge to another will gain some of that energy, depending on how much charge the particle carries. It has to gain the exact amount of energy it took to separate the same charge the particle carries.

The important thing to recognise is that the energy gained does not depend on the particle's path. It can travel in circles, wind itself like a snake or do other crazy stuff, the energy a particle can possibly gain (and possibly loose at the same time due to e.g. friction) is constant between two fixed points.

A ball moving on a shaped landscape behaves the exact same way. Any change in kinetic energy has to be equal to it's mass and change in height, no matter what path it took to get there. Charged particles gain energy equal to their charge and change in ... let's call it "voltage".

Voltage is essentially electric tension. If we put charges in separate containers, e.g. metal plates, we put some tension on the system. Tension that puts a force on the plates and tries to move them. Releasing the tension, allowing the plates to move, would gain those plates exactly the energy we had overcome to separate the charges. But we can release some tension by just taking one charge and moving it to the other plate. That would decrease the tension. This reduction is potential energy that has to go somewhere. It went into the charge we moved by accelerating it and thereby granting it some kinetic energy. At the same time, if we want to separate another charge and put them into the plates, we have to overcome this tension. So afterwards, more tension is stored in the plates.

By having particles traveling between the plates, we can extract the energy stored in this tension. The energy we can extract is always equal to the charge our particle caries and the tension at the time:

• The difference in a particles energy is equal to its charge times the voltage it crossed.

Now we don't need to know no particular electric field in a voltage landscape. As long as we know how high the voltage is at which point, we can just compare two points and figure out the energy of a charged particle. We can even go the other way and ask ourselves how far up particles with a certain energy can get.

We may be interested in the energy a particle gains when it doesn't hit a point of known voltage but passes it by. Since a particle gets faster continuously, passing by a point of known voltage it has to have nearly the same energy as a particle hitting a point of known voltage. So changing our destination by a little changes the energy just slightly. That requires us to assign a voltage to points in empty space between known voltages. Doing this mathematically, we can calculate the complete landscape just by knowing the voltage applied to some parts. After that from knowing where a particle has been and is now, we immediately know it's energy.

When you have a particle not in a vacuum, but inside a conductor, it will constantly loose energy due to friction. At the end of the conductor, the particle will be at pretty much the same kinetic energy, but the conductor will have heated up. The friction constantly removes kinetic energy and deposits it in the form of heat in the conductor.

That friction is actually what makes electric motors move. Magnetic fields force charges on circular paths. A simple motor can be built by having a disk carry a current from its center to its brim, while a magnetic field is pointing perpendicular through the disk. Electrons (the smallest units of negative charge) in a vacuum would just circle round and at some point fly out of the magnetic field. Electrons in a conductor turn the conducting disk because they grind against the conductor material and thereby turn it.

U stands for an electrical power source. The current flows from the center of the disk to the outside while a magnetic field is present. While travelling through the magnetic field, charges are forced into a spiral motion. Friction causes the electrons to lose energy to the disk and thereby turn it.

Since we know the energy one charge (an electron) gains by moving through the disk, we immediately know how much energy the charge can lose throughout the disk. So by just counting the number of charges going through the disk per second, we get the power this motor can deliver. In fact, this is true for any electrical system:

• The power delivered by any electrical system is the applied voltage times the amount of charge per second subject to that voltage: $Power=Voltage\ast <!--\; \ast \; -->ChargePerSecond$, or in scientific notation $P=U\ast <!--\; \ast \; -->I$