Coulomb's law
The axiological blueprint of electrostatics is Coulomb's law, which describes the force amid two point charges. The consequence of the electrostatic force amid two point electric accuse Q1 and Q2 is anon proportional to the artefact of the magnitudes of anniversary allegation and inversely proportional to the apparent breadth of a apple whose ambit is according to the ambit amid the charges:
F = \frac{Q_1Q_2}{4\pi r^2\varepsilon_0}\ ,
where ε0 is a connected alleged the exhaustion permittivity or permittivity of chargeless space, a authentic value:
\varepsilon_0 \ \stackrel{\mathrm{def}}{=}\ \frac {1}{\mu_0 {c_0}^2} = 8.854\ 187\ 817\ \times 10^{-12} in A2s4 kg-1m−3 or C2N−1m−2 or F m−1.
The Coulomb electric force obeys changed aboveboard law like gravity. The Coulomb electric force is amenable for abounding forces: the accustomed force, acquaintance forces, friction, etc all of these armament appear in the alternate allure and abhorrence of answerable particles. The electric connected is 20 orders of consequence greater than the gravitational constant. Hence electricity commonly dominates force at the diminutive and atomic level. However, force dominates in ample bodies, the acumen getting atoms and molecules accept according amount of absolute and abrogating accuse and are accordingly electrically aloof (thus the Coulomb electric force is canceled out).1
edit Electric field
The electric acreage (in units of volts per meter) at a point is authentic as the force (in newtons) per assemblage allegation (in coulombs) on a allegation at that point:
\vec{E} = \frac{\vec{F}}{q}.\,
Or we can say a answerable article in an electric acreage feels a force F=qE
From this analogue and Coulomb's law, it follows that the consequence of the electric acreage E created by a individual point allegation Q is:
E(\vec r) = \frac{Q}{4\pi\ r^2\varepsilon_0}.
The electric acreage produced by a administration of accuse accustomed by the aggregate allegation body \rho (\vec r) is acquired by a amateur basic of a agent function:
\vec E(\vec r) = \frac {1}{4 \pi \varepsilon_0} \iiint \frac {\vec r - \vec r '}{\left \| \vec r - \vec r ' \right \|^3} \rho (\vec r ')\, \operatorname{d}^3 r'.
The amount of the electric acreage gives the force that a answerable atom would feel if it entered the electric field. Electric acreage curve gives the administration of a absolute allegation in the electric field.
edit Gauss's law
Gauss' law states that "the absolute electric alteration through a bankrupt apparent is proportional to the absolute electric allegation amid aural the surface".
Mathematically, Gauss's law takes the anatomy of an basic equation:
\oint_S\vec{E} \cdot\mathrm{d}\vec{A} = \int_V{\rho\over\varepsilon_0}\cdot\mathrm{d}V.
Alternatively, in cogwheel form, the blueprint becomes
\vec{\nabla}\cdot\vec{E} = {\rho\over\varepsilon_0}.
where \vec{\nabla} \cdot is the alteration operator.
edit Poisson's equation
The analogue of electrostatic potential, accumulated with the cogwheel anatomy of Gauss's law (above), provides a accord amid the abeyant φ and the allegation body ρ:
{\nabla}^2 \phi = - {\rho\over\varepsilon_0}.
This accord is a anatomy of Poisson's equation.
edit Laplace's equation
In the absence of unpaired electric charge, the blueprint becomes
{\nabla}^2 \phi = 0,
which is Laplace's equation.
The axiological blueprint of electrostatics is Coulomb's law, which describes the force amid two point charges. The consequence of the electrostatic force amid two point electric accuse Q1 and Q2 is anon proportional to the artefact of the magnitudes of anniversary allegation and inversely proportional to the apparent breadth of a apple whose ambit is according to the ambit amid the charges:
F = \frac{Q_1Q_2}{4\pi r^2\varepsilon_0}\ ,
where ε0 is a connected alleged the exhaustion permittivity or permittivity of chargeless space, a authentic value:
\varepsilon_0 \ \stackrel{\mathrm{def}}{=}\ \frac {1}{\mu_0 {c_0}^2} = 8.854\ 187\ 817\ \times 10^{-12} in A2s4 kg-1m−3 or C2N−1m−2 or F m−1.
The Coulomb electric force obeys changed aboveboard law like gravity. The Coulomb electric force is amenable for abounding forces: the accustomed force, acquaintance forces, friction, etc all of these armament appear in the alternate allure and abhorrence of answerable particles. The electric connected is 20 orders of consequence greater than the gravitational constant. Hence electricity commonly dominates force at the diminutive and atomic level. However, force dominates in ample bodies, the acumen getting atoms and molecules accept according amount of absolute and abrogating accuse and are accordingly electrically aloof (thus the Coulomb electric force is canceled out).1
edit Electric field
The electric acreage (in units of volts per meter) at a point is authentic as the force (in newtons) per assemblage allegation (in coulombs) on a allegation at that point:
\vec{E} = \frac{\vec{F}}{q}.\,
Or we can say a answerable article in an electric acreage feels a force F=qE
From this analogue and Coulomb's law, it follows that the consequence of the electric acreage E created by a individual point allegation Q is:
E(\vec r) = \frac{Q}{4\pi\ r^2\varepsilon_0}.
The electric acreage produced by a administration of accuse accustomed by the aggregate allegation body \rho (\vec r) is acquired by a amateur basic of a agent function:
\vec E(\vec r) = \frac {1}{4 \pi \varepsilon_0} \iiint \frac {\vec r - \vec r '}{\left \| \vec r - \vec r ' \right \|^3} \rho (\vec r ')\, \operatorname{d}^3 r'.
The amount of the electric acreage gives the force that a answerable atom would feel if it entered the electric field. Electric acreage curve gives the administration of a absolute allegation in the electric field.
edit Gauss's law
Gauss' law states that "the absolute electric alteration through a bankrupt apparent is proportional to the absolute electric allegation amid aural the surface".
Mathematically, Gauss's law takes the anatomy of an basic equation:
\oint_S\vec{E} \cdot\mathrm{d}\vec{A} = \int_V{\rho\over\varepsilon_0}\cdot\mathrm{d}V.
Alternatively, in cogwheel form, the blueprint becomes
\vec{\nabla}\cdot\vec{E} = {\rho\over\varepsilon_0}.
where \vec{\nabla} \cdot is the alteration operator.
edit Poisson's equation
The analogue of electrostatic potential, accumulated with the cogwheel anatomy of Gauss's law (above), provides a accord amid the abeyant φ and the allegation body ρ:
{\nabla}^2 \phi = - {\rho\over\varepsilon_0}.
This accord is a anatomy of Poisson's equation.
edit Laplace's equation
In the absence of unpaired electric charge, the blueprint becomes
{\nabla}^2 \phi = 0,
which is Laplace's equation.
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