# Understanding the Fundamentals of Electric Fields...

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1. Jul 24, 2015

### Christina2987

How does an electric charge produce an electric field? How is this field maintained over time without the input of energy? When the charge moves, why is or isn't there any remnant of the field left behind in space?

2. Jul 24, 2015

### tommyxu3

The definition of the electric field $E$ doesn't contain energy. It's the force per Coulomb's charge has. That is, $\vec{E}=\frac{\vec{F}}{q}.$

3. Jul 24, 2015

### tommyxu3

Yes, there is, for the speed of transition of the electric field is finite, which is the speed of light, $c.$

4. Jul 24, 2015

### Staff: Mentor

These are questions that can't really be answered within the domain of physics. I could offer answers of a sort, but they probably won't satisfy you:

(1) We could say that an electric charge produces an electric field by emitting virtual photons. But then you could just ask, "How does an electric charge emit virtual photons?"

(2) We could say that the field is maintained over time without an input of energy because it doesn't take any energy to emit virtual photons (since they're just virtual, not real). But then you could just ask, "How can the charge emit virtual photons without an input of energy?"

(3) We could say that the charge does leave a "remnant" of the field behind, in a sense, because the field fills all space to begin with. But then you could just ask, "Why does the field fill all space?"

What I'm getting at is that explanations in physics (or indeed in any science) will eventually end up at a point where further questions don't have answers, other than "that's just the way it is". The questions you are asking are at that point.

5. Jul 24, 2015

### Staff: Mentor

It's important to understand that a 'field' is a mathematical tool developed to help us explain our observation that certain particles, notably electrons and protons, appear to interact with each other (and several other particles). The specific rules that tell us how they interact were discovered and combined in the 1700's and 1800's to explain electromagnetism in general. We don't know any underlying reason for why two particles with electric charge interact with each other, we just know they do.

The fundamental forces do not require an expenditure of energy to function. In fact, you could say that it is these forces that are responsible for objects having energy, not the other way around.

That's just the way the rules happen to work.

Understand that we have to start somewhere. We have to have some sort of basic, unexplained, accepted facts in order to build up a theory. We can tell you all the rules we know of that explain how two charged particles interact, but we cannot tell you the underlying reason for those rules because we don't know.

6. Jul 25, 2015

### metatrons

These questions are really interesting; although seem simple, some are close to the very nature of the electromagnetic theory, which is very hard to explain. My answers are as follows:

How does an electric charge produce an electric field?

The electric 'field', is a virtue measure of the 'potentials' from the coulomb force. An analogy is one can define a 'gravity field' from earth, which can build up the potential energy of a ball on the table.

General idea is 'force leads to work, work leads to potential energy, and potential energy leads to field.' If you can find a source to provide constant force in any means, you may
also define a certain 'field' for it.

How is this field maintained over time without the input of energy?

First, if the electric-field does not interact with other charges so it does not incur positive or negative 'work', the field should remain. Much like a ball stand still on the table, and the 'gravity field' from the ball to earth shall remain constant.

If the electric-field does incur positive work or negative work, then in general, the field may not maintain without input energy-unless the field source can be approximated as infinitely strong, and the work produced to the external charge are neglect-able.

When the charge moves, why is or isn't there any remnant of the field left behind in space?

Yes, there is remnant field left in space. The simplest understanding is also connecting field to force. If the charge moves (but still exists), the 'potential' of the coulomb force moves accordingly, and the electric field moves accordingly.

It is noteworthy that quantitatively describing charges in moving field is usually difficult or sometimes even impossible (unless the moving field is very regular, such as the periodic rotating field). In most of the cases we only study the field in 'steady states'.