Electricity and magnetism/Electrostatics/Where is the electric potential energy?

Electric potential energy is attributed to electric charges. Is this energy carried by the charges? Is it located on the charges? . Mass is always energy. Energy always has mass. This equation is proven at the end of this book, where it is shown that light trapped in a box increases the mass of the box. Light therefore has a mass equal to its energy divided by . If the electric potential energy were localized on the charges, variations in their energy would cause their mass to vary. But this effect has never been observed. The electric potential energy of a system of charges is in all the space where they produce an electric field, it is carried by the electric field. The volume density of electrical energy in an electrostatic field is where is the electric potential energy contained in a small volume . When we bring two electric charges of the same sign together, we increase the energy of the electric field: 400px If we bring two charges of opposite signs together, we reduce the energy of the electric field. The same is true for the nuclear forces that hold neutrons and protons together in a nucleus. We have to provide them with energy to separate them. This is why their mass is greater when they are separated than when they are united: 400px It takes infinite energy to separate the three quarks that make a proton, or a neutron. This is why we can never observe an isolated quark. Let us show that allows us to correctly calculate the electric potential energy of a charged capacitor: where is the surface area of the capacitor, the distance between the plates, the volume between the plates and the field produced by a surface charge density . Now and so When we define the potential, we are free to choose a point of zero potential. To calculate electric forces, any choice is suitable because two potentials that differ by a constant have the same gradient. But to calculate the energy and the presence of its mass, we are obviously not free to modify the energy of all the charges by choosing another point of zero potential. The point of zero potential must be chosen in such a way that an electric charge can be placed there without making any effort. This is why when we calculate the electrostatic energy of a system of charges, we assume that they are placed in empty space, and we define a zero potential at infinity. The force exerted by electric charges tends to zero at infinity. There is no effort to be made against their electric force if we are very far from them. When a dipole moment is created by the separation of equal and opposite charges, as when charging a capacitor, we can reason as if the charge density were initially zero everywhere. So there is no electric force anywhere. Any point can therefore be chosen as a point of zero potential.