# Bound charges

1. Jun 13, 2005

### heman

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

2. Jun 15, 2005

### 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...

3. Jun 15, 2005

### 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 -

Then there is Quantum Electrodynamics (QED)

Both quotes from Columbia University Press Encyclopedia (from Answers.com)

Last edited: Jun 15, 2005
4. Jun 15, 2005

### 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....

5. Jun 15, 2005

### da_willem

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.

Last edited: Jun 15, 2005
6. Jun 17, 2005

### da_willem

You're welcome...

7. Jun 17, 2005

### 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?

8. Jun 17, 2005

### 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.

9. Jun 17, 2005

### heman

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

10. Jun 17, 2005

### 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.

11. Jun 17, 2005

### 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.