Potential

to see the concerning articles various potentials, to see in fine page

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A potential is a function Scalaire or vectorial taking a value in any point of space characteristic of a conservative Champ of force. Indeed, all the conservative forces derive from a potential. Thus, if the conservative Force $\backslash \; vec\; \{F\}$ and the potential $U$ are noted:

$\backslash \; vec\; \{F\}\; =\; -\; \backslash \; vec\; \{\backslash \; mathrm\; \{grad\}\}\; \backslash \; U$

where $\backslash \; vec\; \{grad\}$ represents the operator definite Gradient according to various notations by:

$\backslash \; vec\; \{\backslash \; mathrm\; \{grad\}\}\; \backslash \; U\; =\; \backslash \; vec\; \backslash \; nabla\; U\; =\; \backslash begin\{pmatrix\}\; \backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; X\}\; \backslash \; \backslash \; \backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; there\}\; \backslash \; \backslash \; \backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; Z\}\; \backslash end\{pmatrix\}$

\ frac {\ partial U} {\ partial X} \ vec {I} + \ frac {\ partial U} {\ partial there} \ vec {J} + \ frac {\ partial U} {\ partial Z} \ vec {K}

$of\; (X,\; there,\; Z)\; =\; \backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; X\}\; dx+\; \backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; there\}\; dy+\; \backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; Z\}\; dz\; =\; (\backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; X\}\; \backslash \; vec\; \{I\}\; +\; \backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; there\}\; \backslash \; vec\; \{J\}\; +\; \backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; Z\}\; \backslash \; vec\; \{K\})\; \backslash \; cdot\; (dx\; \backslash \; vec\; \{I\}\; +dy\; \backslash \; vec\; \{J\}+dz\; \backslash \; vec\; \{K\})\; =\; \backslash \; vec\; \{\backslash \; mathrm\; \{grad\}\}\; \backslash \; U\; \backslash \; cdot\; D\; \backslash \; vec\; R$

where $\backslash \; frac\; \{\backslash \; partial\; U\}\; \{\backslash \; partial\; X\}$ is the Dérivée partial of U (X, there, Z) compared to X.

Gravitational potential

$U\; =\; -\; \backslash \; frac\; \{GM\}\; \{R\}$ where G is the universal constant of gravitation, M is the mass of the object considered, and R is the distance compared to the center of mass of the object considered.

The Poids $p$ of an object of mass m is worth

$P\; =\; -\; m\; \backslash \; cdot\; \backslash \; vec\; \{\backslash \; mathrm\; \{grad\}\}\; \backslash \; U$

Electrostatic potential

See also: Potential electric

The potential V created by a load Q is worth

$$

V (R) = \ frac {Q} {4 \ pi \ epsilon_0 \ left|\ vec {R} \ right|} where ε₀ is the Permittivité vacuum, and R is the distance to the Barycentre load. The electrostatic Force $\backslash \; vec\; \{F\}$ undergone by a load q' is worth:

$$

F = - q' \ cdot \ vec {\ mathrm {grad}} \ V

The expression of V is established starting from the expression of the force of Coulomb between two loads

$$

\ vec {F} = \ frac {q_1 q_2 \ vec {R}} {4 \ pi \ epsilon_0 \ left|\ vec {R} \ right|^3} that one can write

$$

q_1. V_2 (1) = q_2. V_1 (2) = \ frac {q_1 q_2} {4 \ pi \ epsilon_0 \ left|\ vec {R} \ right|} where V₁ (2) is the potential created by 1 into 2 and V₂ (1) is the potential created by 2 into 1 and like mathematically: $\backslash \; vec\; \{grad\}\; (\backslash \; frac\; \{1\}\; \{\backslash \; left|\backslash \; vec\; \{R\}\; \backslash \; right|\})\; =\; \backslash \; vec\; \backslash \; nabla\; (\backslash \; frac\; \{1\}\; \{\backslash \; left|\backslash \; vec\; \{R\}\; \backslash \; right|\})\; =\; -\; \backslash \; frac\; \{\backslash \; vec\; \{R\}\}\; \{\backslash \; left|\backslash \; vec\; \{R\}\; \backslash \; right|^3\}\; \backslash ;$

$$

\ overrightarrow {F_2 (1)} = - \ overrightarrow {grad} \; (q_1. V_2 (1))= \ overrightarrow {grad} \; (q_2. V_1 (2))= - \ overrightarrow {F_1 (2)}

Various electrostatic potential differences can then be defined. One will quote in particular the Potentiel Galvani and the Potentiel Volta.

See too

• potential Energy

• Gravitation

Internal bonds

• Potential of chemical action
• Potential
• Potential electric manpower
• Potential
• Electrochemical potential
• Potential of electrode
• Potential Galvani
• Potential interatomic hydrogen
• Potential
• Potential of mixed ionization
• Potential
• Potential of oxydoreduction or potential Potential redox
• thermodynamics

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