AL physics-Energy of field

1.)電場中擁有的energy到底以咩form存在?(以P.E form?)

In the form of electrostatic energy.

2.)當電場使電荷移動時,電場係gain or loss energy?而且gain form邊度or loss to 邊度.(Please 分清唔同case to explain e.g.)+/-charge act by field produce by +/- charge)

Each charge has associated with it an electric field. The movement of charges (whether it is a repuslion or an attraction) is the result of interaction of electric fields of the two charges. Under such situation, the electrostatic energy would trnasformed into mechanic energy (kinetic energy) of the charges.

3.)場中的energy 如何傳送到其他野到?

As said above, energy transfer is a result of interaction between electric fields associated with the charges.


4.)如何能使一個場的energy 完全用盡(有可能嗎?) (If yes, please give some examples and what will happens.)

Discharging an object removes all the energy associated with the electric field.

The energy density (per unit volume) of electromagnetic field is given by

圖片參考：http://imgcld.yimg.com/8/n/HA05726829/o/701105260010713873451610.jpg
....................(1)
in Gaussian units. (For S.I. units, replace 4 pi by electric permittivity and B by cB.) This means that electromagnetic field carries energy of their own even in the absence of charge. For example, light is a transverse oscillation of electric and magnetic field, and the above equation tells the classical energy of light.

Examples in electric circuits are capacitors and inductors. Energy are stored in the devices in the form of electric and magnetic field. They gain or loss energy from or to the movement of electrons in the circuits. The transfer of energy is due to the coupling between field and charge.

圖片參考：http://imgcld.yimg.com/8/n/HA05726829/o/701105260010713873451611.jpg
..................(2)
So there are (positive or negative) work done by the field to charge.

A theory of plasma could illustrate the transfer of energy between field and charge. Consider a uniform neutral gas of matter, where the positive charges (protons) are fixed and the negative ones (electrons) are free. So there is a uniform electric field and current density in the medium.

Let m and e be mass and charge of electron, n be the number density. The Ampere's law of Maxwell's equation is

圖片參考：http://imgcld.yimg.com/8/n/HA05726829/o/701105260010713873451622.jpg
.....................(3)
where J = env is the current density, v is the velocity of electrons. (Here, we assume B=0.) The force equation tells us

圖片參考：http://imgcld.yimg.com/8/n/HA05726829/o/701105260010713873451623.jpg
...............(4)
Combining (3,4), we have a harmonic motion

圖片參考：http://imgcld.yimg.com/8/n/HA05726829/o/701105260010713873451624.jpg
............(5)
It has solution

圖片參考：http://imgcld.yimg.com/8/n/HA05726829/o/701105260010713873451635.jpg
........(6)
The kinetic energy density of the moving charge is clearly

圖片參考：http://imgcld.yimg.com/8/n/HA05726829/o/701105260010713873451636.jpg
...........(7)
Plug (6) into (1,7), and simplify using the plasma frequency (5). The energy densities for field and charge are

圖片參考：http://imgcld.yimg.com/8/n/HA05726829/o/701105260010713873451647.jpg


So you can see that it is exactly like SHM. The energy keep switching between field and charge (like PE and KE). And the two add up to a constant.

Finally, even in vacuum where there is no charge, when there is field, there is energy. So de-energizing the field actually means removing the field.