Significance of electric field

Question

Two charges experience Coulomb force. We say electric field $E=F/q$ at this point and at that point and so this is the field around the charge. But why do we introduce a new concept when we can just solve anything with just the force? Why do we talk about $E$ every time? I mean this is one charge, that is another charge, and this is force acting on it. End of story. Why do we talk about $E$ due to various charge distributions and solve countless problems on finding the net field. Why?

Answer 1

When electric charges were first studied, scientists described effects just as you want to: electric charges exerting forces on each other. It wasn't until Michael Faraday came up with the idea of lines of force around 1855 that scientists began to rethink interactions that take place between separated objects. When one thinks about forces that affect objects that are not touching each other--gravity, electricity, magnetism--one begins to wonder: how do these separated objects affect each other? How do charged objects know about each other so that they may repel or attract? How does the Sun reach across empty space to hold Earth in orbit? Famously, Isaac Newton didn't even try to guess at this last question; he just postulated that there was a force and calculated.

However, when the concept of a field is introduced, the mystery can be answered. For example, every object with an electric charge creates an electric field in the space surrounding it. When another electrically charged object is placed in that space, it is the electric field at that location that puts a force on the second charge. There is no need for two separated charges to somehow find out where the other is in order to accelerate correctly. Each electric charge just has to feel the electric field in its own location.

The second consequence of introducing the field concept is that the field itself becomes a subject of study. The question becomes: is this field a physical object like electric charges? Is a universe with action-at-a-distance electrical interactions different from a universe with electric fields?

Consider a universe that is totally empty except for one electron. In a universe with action-at-a-distance electrical interactions, the electron's electric charge is completely irrelevant. There are no other electrical charges for it to push on nor to be pushed by. If the electron gets shaken, nothing happens.

Now add in an electric fields. The electron has an electric charge, so there is an electric field that fills the whole universe around it. Is this universe different? There are still no other charges for the electric field to push, nor are there electric fields from other charges to push the electron. However, the electric field is a physical entity. If the electron is shaken back and forth, the electric field is shaken as well. In the same way that shaking a rope causes a wave to propagate along it, so does shaking an electric field create waves to travel away from the shaken charge. The waves that are created by shaking an electric field is what we call light.

Electric fields are real physical entities in our universe. In fact, to continue the single-electron universe example, once the light is created by shaking the electron, the electron can be removed from the universe and the light wave will still exist--propagating away from where the electron used to be. Undulating electric fields can exist where there are no electric charges, so we need a way to describe electric fields separately from electric charges.

Answer 2

Ok, let us take a very similar example from real life in order to under their importance.

We must had played with two magnets in some part of life trying to make them attract/repel.How these two magnets are attracting each other? Even if we take these magnets in vacuum, they still tend to attract/repel each other!

How they are interacting with each other, there is nothing there except the two magnets?

What is the reason behind the force you feel in your hand while you keep them close enough?

How one can calculate the F force without knowing their source of attraction?

The above example is of Magnetic field of the magnets. If you haven't taught about Magnetic field, these questions may baffle your mind. I took this example because ,the things we learn in Electrostatics are kind of abstract systems for a typical person, we will not find two charges here and there to play with.

In the similar way, we can ask how two charges attract each other placed at a distance.

In the image above, if you keep bar magnet on a uniformly spread fine iron particles, then you will see that the bar magnet is exerting the force on those iron filling. You can also consider an similar but abstract situation for two point charges. These patterns were called lines of force in the initial years of discovery.

The term 'Electric Field' was introduced to represent the force at every point around the system. One cannot see this field, because it a abstract concept that we made in order to explain the forces due to charges. But without this you will not be able to explain, what actually is exerting force in an empty space.

Also, we talk about E of Dipoles, Charged rings, etc because you just were introduced to the concept of E field , and in order to further understand how an electric field behaves for different configurations you need to solve the mathematics behind the problems. You cannot be given a real life problem on E field because real life problems are way more difficult than a newly taught student may imagine. Hence we try to understand these concepts by considering the simple systems that may seem to be abstract and hardly seen in real life, but they help in understanding concepts.