What is the reality of the Electric Force & Field?

[Achintya]

Please help. Thank you.

 

[phyzguy]

In the 1800's, scientists spent a lot of time trying to create "mechanistic" models of the type you are proposing. Either these models added mothing, or they predicted effects which are not observed. Today we (at least most of us) no longer believe in models of this type. The electric field is a phenomenon that has a magnitude and direction at each point is space. We can calculate the electric field if we know the distribution of changes everywhere. If we know the electric field, we can predict how charges will move. That's all there is to it. If you like, the electric field is the "something" that causes the particle to experience forces.

 

[Achintya]

In the 1800's, scientists spent a lot of time trying to create "mechanistic" models of the type you are proposing. Either these models added mothing, or they predicted effects which are not observed. Today we (at least most of us) no longer believe in models of this type. The electric field is a phenomenon that has a magnitude and direction at each point is space. We can calculate the electric field if we know the distribution of changes everywhere. If we know the electric field, we can predict how charges will move. That's all there is to it. If you like, the electric field is the "something" that causes the particle to experience forces.

Is it somehow related to photons or anything like that?

 

[PeroK]

Is it somehow related to photons or anything like that?

In Classical Electromagnetism, the electric field causes the electric force. In Quantum Electrodynamics, which is a more fundamental theory, the force is the result of the interaction of charged particle through the exchange of photons.

 

[vanhees71]

First of all, at this stage of learning about electromagnetism forget about photons. The only way to understand photons correctly is relativistic quantum field theory (or quantum electrodynamics as one of its paradigmatic applications), and this is a pretty advanced topic.

The field concept has been discovered by Faraday in an induitive way based on a lot of experience with experiments and observations of phenomena related to electricity and magnetism. The fundamental idea is that there are no actions at a distance but only local ones.

Let's start with the most simple case of electrostatics. Take some point-like charge at some place. Then the observation is that another point charge "feels" the Coulomb force, whose magnitude goes like $1/r^2$ (with $r$ the distance between the two charges) and proportional to the product of the two charges $q_1 q_2$. The direction is along the connecting line between the charge and it's attractive (repulsive) if $q_1 q_2<0$ ($q_1 q_2 >0$). The formula is
$$\vec{F}_1=\frac{q_1 q_2}{4 \pi \epsilon_0} \frac{\vec{r}_1-\vec{r}_2}{|\vec{r}_1-\vec{r}_2|^3}$$
for the force acting on charge $q_1$ due to the charge $q_2$.

This is very similar to Newton's law of the gravitational interaction, and that's why first the physicists like Ampere and Weber thought about the Coulomb field as an "action at a distance", though even Newton had already his doubts about this idea.

Faraday had another point of view: He interpreted the force differently, i.e., he assumed that with the charge comes also an electric field around it, defined at any place $\vec{r}$. For a charge $q_2$ at rest located at $\vec{r}_2$ this field is given by
$$\vec{E}(\vec{r})= \frac{q_2}{4 \pi \epsilon_0} \frac{\vec{r}-\vec{r}_2}{|\vec{r}-\vec{r}_3|}.$$
Now the force acting on charge $q_1$ located at $\vec{r}_1$ is interpreted as a local effect due to this electric field at the position of the charge, i.e.,
$$\vec{F}_1=q_1 \vec{E}(\vec{r}_1).$$
This shows that the charge has two physical consequences (here formulated for charges at rest, i.e., electrostatics):

(a) it's the source of an electrostatic field; each point charge contributes a Coulomb field as described above. The Coulomb fields of several point charges simply vectorially add up to the total electrostatic field $\vec{E}(\vec{r})$, defined at any point $\vec{r}$ (except at the locations of the point charges, where the field diverges, but that's an artifact of our idealized assumption of a point charge, which is a somewhat more complicated issue, which is again finally resolved by quantum field theory).

(b) On another charge $q$ (often called a "test charge") an electric force is acting due to the value of the electric field at the location of this test charge.

This makes the interaction among charges local, i.e., mediated by the field.

In a similar way you can define the magnetic force on moving point charges by introducing the concept of the magnetic field, which again is a local action: $\vec{F}_1^{(\text{mag})}=q \vec{v}_1 \times \vec{B}(\vec{r}_1)$.

It took some years for Maxwell to find a complete set of equations to describe the most general case of time-dependent electric and magnetic fields and arbitrarily moving charges, the Maxwell equations. The field concept turned out to be crucial since in Maxwell's theory the electric and magnetic field have to be seen as one entity, the electromagnetic field, and it's a dynamical entity in its own right, i.e., it's not bound to charges at all but can "travel" as an electromagnetic wave through a vacuum. As it also turned out, light is nothing else than such an electromagnetic wave, i.e., with Faraday's and Maxwell's insights, not only electricity and magnetism where made a unified concept of the electromagnetic field but also the entire realm of optics has been subsumed into the theory of electromagnetic fields, which are caused by electric charge-current distributions and act themselves on charge-current distributions by the corresponding Lorentz force in a local way.

This concept of local actions rather than actions at a distance a la Newton later proved crucial even further, when Einstein (after important previous work by Lorentz, FitzGerald, Heaviside, Poincare et al) discovered the special theory of relativity when analyzing Maxwell's equations further. According to this theory actions at a distance cannot be fully true, because nothing can travel faster than a certain "limiting speed", and all observations indicate that this limiting speed is the speed of light, i.e., the phase velocity of electromagnetic waves in a vacuum. Thus the only really successful description of the fundamental forces (among them the electromagnetic interacion) so far only possible through the field concept and locality, i.e., interactions among particles are described as "mediated" by fields.