# Charge density and electromagnetics

1. Jun 19, 2009

### GRB 080319B

What is the difference between charge density and charge carrier density? If each electron has an elementary charge of -1 (natural units), and the electric field and voltage are manifestations of the effects of charge, then why is charge referred to as seemingly seperate of electrons in text? (in this post, I will be asking about charge wrt electrons, not protons or other charge carriers)

If an electric field's strength is based on the amount of charge, then wouldn't that necessarily mean the strength is resultant from the specific number of electrons at a specific spot generating the surrounding field? Is there a way to generate a greater electric field strength without more electrons? Is the potential energy of the field generated by the amount of electrons? Is a stronger electric field necessarily caused by more electrons?

As for voltage, would the electrostatic potential simply be the relative difference between the amount of electrons present in separate materials? Is there a maximum difference (voltage) that a material can have ( 0 electrons vs most electrons a material can hold)? Is there a maximum electron density for any physical material? Is the only way to increase the charge of a capacitor is increase the number of electrons or electron density of the plate?

Does the electric field flow around the electrons and is not dependent on their exact position, or just around the wire? http://amasci.com/miscon/eleca.html#current"

I attempted to read a calculus based physics book on electromagnetics, but did not make much headway. The book treats charge as if is some mathematical concept that exists without physical form (the electron or any charged particle). Is this true? Is charge some type of free-floating ether that manifests itself as the electric field and creates electrostatic potential independent of electrons and other charge carriers? Most of my physics knowledge comes from a conceptual physics book and this http://amasci.com/miscon/elect.html" and have taken two semesters of calculus, so I apologize if I have made some serious errors in my understanding or am asking questions that are too advanced for my mathematics or physics level. I have used the site mentioned above extensively, and am also wondering how good of a source it is for learning about electromagnetics.

Thank you

Last edited by a moderator: Apr 24, 2017
2. Jun 19, 2009

### Bob S

Suppose I had two copper plates, each 1 meter square, and separated by 1 millimeter. Now suppose I take a Coulomb of electrons (about 6.25 x 1018) from one plate and moved them to the other**. So one plate has an excess of electrons (one Coulomb), and the other plate a deficit of electrons. Let's call the deficit of electrons "negatrons" for lack of a better name. There is now an electric field between the two plates, trying to pull the two plates together. The electric field is due to the charges on the plates. Because copper is a conductor, the electrons and "negatrons" both freely move around. Because of the electric field, there is an electric potential (voltage, equal to electric field times separation) between the plates. Now suppose I pull these two copper plates further apart, from 1 millimeter to 1 centimeter. There is a large force attracting the two plates together, so I have to do a lot of work (F dx) to pull them apart. But the charge on the plates (One Coulomb) has not changed. By doing this work, the voltage between the two plates has increased by a factor of 10. So charges are real things, like electrons and "negatrons" (deficits of electrons). Charges create electric fields, and voltage is just work we have done to separate the charges. When you plug in a 120 watt light bulb (where electricity is 120 volts), there is (are) a Coulomb of electrons flowing through the light bulb every second. The voltage, 120 volts in this case, is just potential we have created by using big electromechanical machines (generators) to pull the charges apart by doing work (F dx). I hope this does not confuse you more.

63 grams of copper contains about 3 million Coulombs of electrons, so 1 Coulomb is a small amount. each copper atom has 29 electrons.

3. Jun 19, 2009

### GRB 080319B

In your example, when you say that you move 1C of electrons so that one plate has an excess of electrons, and then that an electric field is created by the separation of the charges, is it the charge of each electron that was moved that causes this field? In your example, you switch from talking about coulombs of electrons to charges, and I just wanted to make sure that one can't increase the charge of one plate without moving the equivalent amount of electrons, since each electron has a elementary charge of http://en.wikipedia.org/wiki/Elementary_charge" [Broken], and you move 6.25 x 1018 coulombs of electrons.

So does the charge quantified in each electron moved creates the voltage between the two plates, since you had to do work to move them to one plate? Is voltage then just the work done to move electrons, or do the electrons have to already be separated and an electric field established (separate, charged plates in your capacitor example) in order for the work done to be considered voltage?

Is there no electric field at all in the setup until you move the coulomb of electrons to one plate or just no electric field between the plates until you do so? Does the electric field between the two plates weaken with distance, and if so, does this correspond to a lesser and lesser increase in voltage as the plates are pulled farther apart do to less work being done?

So is charge analogous to the mass of a particle? And the electric field created analogous to the gravitational field (Newtonian force) created by a particle with mass?

Last edited by a moderator: May 4, 2017
4. Jun 20, 2009

### Bob S

When you separate a - charge and a + charge, you do work. When you separate charges, you create an electric field. When you separaate the charges more, you do not create more electric field. The electric field is proportional to the quantity of electric charge, nothing more. There is an attractive force between these charges. When you separate the charges more, your work increases the voltage between them. This work does not increase the amount of charge, or increase the electric field. I was talking about moving 1 Coulomb of charge.
By separating an electron and the "hole" (absence of electron), you do work. Work (force time distance) is energy. The energy is stored as voltage.
There is no electric field at all until one electron is moved from one capacitor plate to the other. Electric field does not weaken as the plates are separated. Electric field is proportional to the number of charges, not distance.

The charge of one electron is one of the fundamental constants, as is its mass. A graviton (if found) will also be a fundamental constant. Electric fields or gravitational fields are proportional to the number of charges or gravitons. But electric fields and gravitational fields differ in fundamental ways.

Last edited by a moderator: May 4, 2017
5. Jun 20, 2009

### GRB 080319B

Thank you very much for your help Bob S. I think my problem is in understanding the difference between the electromagnetic force and the electromagnetic field. The electromagnetic force varies by distance in accordance with the inverse square law (weakens by distance like gravitational force). The electromagnetic field is only set up when opposite charges are separated, and its strength is proportional to the number of charges. The electromagnetic field is dissimilar to the gravitational field in that it is only set up when opposite charges are separated and not permanently existent like the gravitational field due to all mass having the same attractive "charge". Voltage then is the potential energy stored (in or between?) the charges by the work done to separate them against the electromagnetic force. The separation of charges sets up the electromagnetic field between them that will direct them together once a circuit is made, converting the voltage into kinetic energy as the charges converge. Feel free to make any corrections to the above statements, as they are really questions in statement form.

Is more work done, and more voltage obtained, by the first incremental distances of separating two charges as opposed to separation at greater distances due to the fact that the force is weakening by the inverse square law? Will eventually no voltage be accrued as the strength of the force approaches 0 (or as distance separating the charges approaches infinity)? Does greater voltage mean greater speed of converging charges (like greater gravitational potential energy will mean greater impact speed after falling)?

Thank you.

Last edited: Jun 20, 2009