# Bound charges

#### heman

what is basically the concept of bound charges in electrodynamics??

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#### heman

actually i wasn't specific so how could i get replies....i read that topic i am familiar with the formulas and also done problems on that topic but i wanna know.....in reality what happens....why are they called bound...i want to know what happens physically,nothing more...

Aspiring to see urs replies and Thankful for devoting yours time...

#### Astronuc

Staff Emeritus
Do you mean bound charges as the electrons in an atom are bound? In that case, quantum mechanics provides the explanation.

Electrodynamics is the study of moving electric charges and their interaction with magnetic and electric fields.

Or a more complex answer -

electrodynamics, study of phenomena associated with charged bodies in motion and varying electric and magnetic fields (see charge; electricity); since a moving charge produces a magnetic field, electrodynamics is concerned with effects such as magnetism, electromagnetic radiation, and electromagnetic induction, including such practical applications as the electric generator and the electric motor. This area of electrodynamics, often known as classical electrodynamics, was first systematically explained by the physicist James Clerk Maxwell. Maxwell's equations, a set of differential equations, describe the phenomena of this area with great generality. A more recent development is quantum electrodynamics, which was formulated to explain the interaction of electromagnetic radiation with matter, to which the laws of the quantum theory apply. The physicists P. A. M. Dirac, W. Heisenberg, and W. Pauli were the pioneers in the formulation of quantum electrodynamics. When the velocities of the charged particles under consideration become comparable with the speed of light, corrections involving the theory of relativity must be made; this branch of the theory is called relativistic electrodynamics. It is applied to phenomena involved with particle accelerators and with electron tubes that are subject to high voltages and carry heavy currents.
Then there is Quantum Electrodynamics (QED)

Quantum electrodynamics (QED), quantum field theory that describes the properties of electromagnetic radiation and its interaction with electrically charged matter in the framework of quantum theory. QED deals with processes involving the creation of elementary particles from electromagnetic energy, and with the reverse processes in which a particle and its antiparticle annihilate each other and produce energy. The fundamental equations of QED apply to the emission and absorption of light by atoms and the basic interactions of light with electrons and other elementary particles. Charged particles interact by emitting and absorbing photons, the particles of light that transmit electromagnetic forces. For this reason, QED is also known as the quantum theory of light.

QED is based on the elements of quantum mechanics laid down by such physicists as P. A. M. Dirac, W. Heisenberg, and W. Pauli during the 1920s, when photons were first postulated. In 1928 Dirac discovered an equation describing the motion of electrons that incorporated both the requirements of quantum theory and the theory of special relativity. During the 1930s, however, it became clear that QED as it was then postulated gave the wrong answers for some relatively elementary problems. For example, although QED correctly described the magnetic properties of the electron and its antiparticle, the positron, it proved difficult to calculate specific physical quantities such as the mass and charge of the particles. It was not until the late 1940s, when experiments conducted during World War II that had used microwave techniques stimulated further work, that these difficulties were resolved. Proceeding independently, Freeman J. Dyson, Richard P. Feynman and Julian S. Schwinger in the United States and Shinichiro Tomonaga in Japan refined and fully developed QED. They showed that two charged particles can interact in a series of processes of increasing complexity, and that each of these processes can be represented graphically through a diagramming technique developed by Feynman. Not only do these diagrams provide an intuitive picture of the process but they show how to precisely calculate the variables involved. The mathematical structures of QED later were adapted to the study of the strong interactions between quarks, which is called quantum chromodynamics.

Bibliography

See R. P. Feynman, QED (1985); P. W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics (1994); S. S. Schweber, QED and the Men Who Made It: Dyson, Feynman, Schwinger, and Tomonaga (1994); G. Scharf, Finite Quantum Electrodynamics: The Causal Approach (1995).
Both quotes from Columbia University Press Encyclopedia (from Answers.com)

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#### heman

Thanx for it Astro,,,
urs web browsing skills are very gr8..
But i revolved in Dielectrics in Electricity and more specificly in Polarization...
When Polarization exists we solve problems with bound charges...
I am not clear with it physically...,my book did not came with good explanation....

#### da_willem

heman said:
i wanna know.....in reality what happens....why are they called bound...i want to know what happens physically,nothing more...

Aspiring to see urs replies and Thankful for devoting yours time...
In a polarized object the molecules consitute electric dipoles which are aligned. A dipole can be viewed as a charge distribution with some negative charge on one side and some positive charge on the opposite side. Now if all the dipoles in an object are aligned this will mean these charges will cancel, i.e. the negative charge on one dipole will be cancelled by the positive charge on its neighbouring dipole. Except at the surface of the object where no cancellation is possible. This is why the polarized object can be described by a "bound surface charge":

$$\sigma _b = \vec{P} \cdot \hat{n}$$

which is proportional to the polarization and is largest where the surface of the object and the polarization are aligned.

Now if the strength of the individual dipoles is not the same the cancellation will not be complete and there will be some net charge density proportional to the mismatch (the divergence of the polarization):

$$\rho _b = - \nabla \cdot \vec{ P}$$

which is called the bound charge density.

The bound charge thus comes from the alignment of polar molecules in a polarized object. They are called bound because they cannot be removed. Chop a bar polarized along its axis in two and its bound surface charge and bound charge density will be the same.

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#### da_willem

You're welcome...

#### heman

Thanx Willem,,It was very nicely explained..
But i still have confusions when Polarisation is varying,,
In this case they shouldn't cancel...
So why will they be called bound?

#### Doruk

Heman, you might be getting better replies if your curiosities were posted on engineering forum since the "bound charge" concept is more widely used in "engineering electromagnetics". (This was also actually the name of the course that we've been introduced to the subject at the collage.)

They're called "bound" because they can not move freely, -move to positions of equilibrium in response to the fields- as the charges do in the conductors.

#### heman

You in which Semester Doruk ,,Is this an Independent Subject>?

#### Doruk

Heman, It is my last semester. Surely, not independant of physics, but a better way to put it, would be saying that, it is heavily related to engineering.

#### masudr

A bound system is where the total potential energy of the system:
$$E=\frac{1}{2}\sum_n \frac{q_iq_j}{4\pi\epsilon_0r_{i,j}^2}$$
is below 0; this means that as t tends to infinity, the charges will not be an infinite distance apart from each other.

"Bound charges"

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