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See next post, please ...



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--Last edited by saucer on 2009-04-02 14:14:13 --

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Potential -

As entities described as vector fields occur often in physics, it is often useful to work with their potentials.

For instance, some force fields exert forces on a body equal to the product of the field and some invariant scalar property of the body.

As a body moves through such a force field, it rises and falls in the associated potential. The energy gained or lost by the body through mechanical work performed by the force is defined as its potential energy. It is then possible, in the case of a particle subjected to a known field, to speak directly of its change in energy between two points, without resorting to kinematics, which can be computationally difficult.

The gravitational field is a notable example of such a field. The electric field also behaves this way in many cases, though in the general case it does not



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Potential energy -

A book on a table has greater gravitational potential energy than the same book on the floor. However the same book has less gravitational potential energy than if it were even higher, say upstairs. In raising the book from the floor to the table, work was done by someone which is now stored as potential energy. (This energy was provided by the chemical energy stored in food). The presence of this potential energy could be demonstrated by sliding the book off the table. The book would gain kinetic energy from its velocity until it reached the floor. The kinetic energy would then be converted into heat and sound by the impact.

In another example in Wales at Dinorwig there are two lakes, one higher than the other. At times when surplus electricity is not required (and so is cheap), water is pumped to the higher lake. At times of peak demand for electricity, the water flows through turbines and generates electricity once more (see also pumped storage). (The process is not completely efficient and much of the original energy from the surplus electricity is wasted by friction). In this example the potential energy is stored by doing work against the force of gravity.

The factors that affect the amount of gravitational potential energy that is created are: the mass of the object, the distance that it is raised and the gravitational field strength. Raising the same object to the same height on the Moon would require less energy than on earth because the force of gravity on the Moon's surface is less.





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Binding energy -

Binding energy is the energy required to disassemble a whole into separate parts. A bound system has a lower potential energy than its constituent parts; this is what keeps the system together; it corresponds to a positive binding energy.

At the nuclear level, binding energy is derived from the strong nuclear force and is the energy required to disassemble a nucleus into neutrons and protons. At the atomic level, binding energy is derived from electromagnetic interaction and is the energy required to disassemble an atom into electrons and a nucleus. In astrophysics, gravitational binding energy of a celestial body is the energy required to disassemble it into space debris, not to be confused with the gravitational potential energy to separate e.g. a celestial body and a satellite to infinite distance, keeping each intact.

Because a bound system is at a lower energy level, its mass must be less than its unbound constituents. Nuclear binding energy can be computed from the difference in mass of a nucleus, and the sum of the mass of the neutrons and protons that make up the nucleus. Once this mass difference (also called the mass defect) is known, Einstein's formula (E = mc²) can then be used to compute the binding energy of any nucleus.

The energy given off during either nuclear fusion or nuclear fission is the difference between the binding energies of the fuel and the fusion or fission products.

Potential Fields              (Unknown Source)              
Fields
A field is a set of functions of space and time.

We are concerned with 2 kinds of fields:

Material fields describe some property at a point of the material and at a given time (intensive quantity)

Examples: density, porosity, magnetic susceptibility, temperature; not a material property: mass, heat; these are extensive quantities (depend on extent of material)
Force fields describe forces that act at each point of space at a given time

Examples: gravity, magnetic field, electrostatic field
Fields can be scalar or vector or tensor

A vector field can be described in terms of field lines (or lines of flow, or lines of force or flux lines). These are lines that are tangent at every point to the vector field.

Potential Theory
Concept of potential

Example: Consider map of ski area: put arrows everywhere giving magnitude and direction of slope; It is easier just to give elevation at each point!

In 1-D  

In 3-D:

   

2-D example of relationship between scalar potential and vector field

[Note: Ñ is the "del" operator or gradient operator; it is always a vector quantity; sometimes it is written with an arrow over it, or boldfaced, to indicate that it is a vector operator]  Thus we see that a scalar field (elevation) can give rise to a vector field (slope)

Another example: temperature field (scalar),  heat flow field (vector), where



Conservative Fields
For force fields (vector fields) it can be shown that if the force field is conservative, it may be (and must be) represented as the gradient of a scalar field.

All force fields derived from scalar field are conservative
All conservative fields can be derived from scalar


Let's show that a force field derived from scalar is conservative:

Conservative:



Stokes Theorem: [Kaplan, Advanced Calculus, 2nd Ed., p. 344 ff.]



If there are no singularities in F, then U must be continuous and differentiable, so order of differentiation doesn't matter, and



and therefore F is conservative.  

--Last edited by us2u on 2006-12-29 15:37:27 --

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Electron Binding Energies

Electron binding energies in eV for the elements in their natural forms

http://xray.uu.se/hypertext/EBindEnergies.html



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--Last edited by saucer on 2007-08-26 23:52:21 --

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http://online.physics.uiuc.edu/courses/phys111/fall03/Lectures/Lect11/sld011.htm  


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