# Is the voltage a result of the existence of the electrical field or is it vice-versa?

Sorry for my question that may be a bit vague but In my school book there are these two definitions:

The direct current results from the movement of free electrons so the overall movement be in one direction from the low electrical potential to the high electrical potential because of the existence of an electrical field that results from the applied voltage.

And the A.C results from ... And the vibrational movement of electrons results from the changing electrical field in both value and direction which spread at the speed of light around the conductor and this change in electrical field results from the change of the value and sign of voltage between the two electrodes of the power supply.

And my question is does the electrical field arises from the existence of voltage or is it vice-versa. As I understand the electrical potential is the potential electrical energy that a charge has if put near another charge. Doesn't that makes it a result of the existence of an electrical field ?

P.S: The book isn't in English so what is written above is a translation I did in a very humble manner

• The voltage and the electric field describe the same phenomenon. The electric field corresponds to the so-called gradient in voltage, which is just the change in voltage per unit distance. Aug 25 '17 at 17:02

Your question is rather philosophical. Both point of views are fine and it really doesn't matter. However, I would argue that the electric field is "more fundamental", because it has a more prominent role in the modern description of physical phenomena. Especially due to Maxwell and his equations describing the electrodynamics.

• Could it also be argued that the electric field is more fundamental since the value of the potential is arbitrary up to a constant and the electric field can be defined as a definite value? Aug 25 '17 at 17:14
• That depends on your personality. In other words, would you argue that forces are more fundamental than momentums since the value of velocity vectors is arbitrary up to a (vector) constant but the acceleration can be defined as a definite value? Aug 25 '17 at 17:20

Causal language ("A causes B") does not make sense when we're trying to switch between two equivalent descriptions of how the world works.

Newton gave us this elegant description of how the world works in terms of particles: their positions and velocities and, most importantly, their forces on each other. These quantities are vectors obeying certain laws which we can discover.

Now it turns out that this is mathematically equivalent, in many cases, to a different description of how the world works in terms of energies obeying certain laws we can discover. I think you're at a pre-undergraduate education level about these things so usually we only provide a couple of "highlights" of looking at the world in this way. So, we tell you that there is a mysterious number called the total energy which in most circumstances does not change; we do not tell you that the reason that it does not change is because those energy-laws have a special "symmetry" to them called "time translation symmetry" -- this is a fancy way of saying that the energy-laws do not change over time. We also do not tell you how to recover the equations of motion that Newton's laws produce from this picture -- there are two ways to do it, the "Hamiltonian" formulation based on the sum of kinetic and potential energy, and the "Lagrangian" formulation based on the difference between kinetic and potential energy.

Not all things are quite so easy to deal with in the energy picture -- in particular friction forces are much harder to deal with in the energy picture. (In some ways they simplify that picture immensely into a "minimum potential energy principle -- but they make it much harder to derive equations of motion in several common contexts. It turns out that when you do deal with them you discover things like Brownian motion that are somewhat harder to deal with in the force picture, too -- so this complexity is intrinsic to both approaches but we happen to be better at dealing with one or the other in various limits.)

Between these two different-but-equivalent ways of describing the world, there can be no "causes". Both descriptions predict the same motion of the particles; you can either imagine that the energy picture is a useful short-hand way of talking about the underlying force laws, or that the force picture is a useful short-hand way of talking about the underlying energy laws -- whatever suits your purpose. Mechanical engineers are much more likely to talk about forces and stresses and strains and the like, dealing with the world in Newton's terms. People who study electrical transport through nano-scale devices are much more likely to talk about energy levels and band gaps and the like, dealing with the world in energy terms.

There is a branch of physics right now, called quantum physics, which works much better with the "energy" descriptions than it does with the "force" descriptions. For example when you try to form the energy-picture for the electromagnetic theory of Maxwell, which is normally phrased in terms of force fields, you find that to treat magnetism properly you must deal with a new field called the 'vector potential', as well as the usual 'scalar potential' field. It turns out that there are quantum effects like the Aharonov-Bohm effect which depend on the vector potential directly, with none of the usual barriers between the "energy picture" and the "force picture" that would normally allow an easy interpretation in terms of forces. This is the only respect that I know of where the energy picture has a clear "one up" on the force picture, and even that is somewhat tenuous.

• Thank you ! You pointed me that my question means does force result from energy or vice-versa? And that looks quite big.
– MSh
Aug 25 '17 at 17:34