|
[[Skeda:Bcoulomb.png|thumb|right|300px|[[Peshore torsioni|Peshorja e torsioni]] e Kulombit]]
Neqoftese drejtimi i force nuk na hyn në pune atëherë forma e thjeshtuar, [[skalare]], e versionit të ligjit të Kulombit mjafton. Madhësia e forcës mbi një ngarkese, <math>\scriptstyle{q_1}scriptstyle__L_CURLY__q_1__R_CURLY__</math>, për shkak të pranisë te një ngarkese të dyte, <math>\scriptstyle{q_2}scriptstyle__L_CURLY__q_2__R_CURLY__</math>, jepet nga moduli i
:<math>F = {1__L_CURLY__1 \over 4\pi\varepsilon_0}varepsilon_0__R_CURLY__\frac{q_1q_2}{rfrac__L_CURLY__q_1q_2__R_CURLY____L_CURLY__r^2}2__R_CURLY__</math>,
ku <math>\scriptstyle{r}scriptstyle__L_CURLY__r__R_CURLY__</math> është ndarja e ngarkesave dhe <math>\scriptstyle{scriptstyle__L_CURLY__\varepsilon_0}varepsilon_0__R_CURLY__</math> është [[konstantja elektrike]]. Një forcë pozitive implikon një bashkëveprim shtytës, kurse një forcë negative tregon një bashkëveprim terheqes.<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefor.html#c1 Coulomb's law], Hyperphysics</ref>
Faktori, (<math>\scriptstyle{k_e}scriptstyle__L_CURLY__k_e__R_CURLY__</math>) i njohur si konstantja e Kulombit, është :
:<math>
\begin__L_CURLY__align__R_CURLY__
\begin{align}
k_e &= \frac{1}{4frac__L_CURLY__1__R_CURLY____L_CURLY__4\pi\varepsilon_0} = \frac{frac__L_CURLY__\mu_0\ {c_0}__L_CURLY__c_0__R_CURLY__^2}{42__R_CURLY____L_CURLY__4 \pi} = 10^{__L_CURLY__-7}7__R_CURLY__\ {c_0}__L_CURLY__c_0__R_CURLY__^2 \\
&= 8.987\ 551\ 787\ \times 10^9 \\
\end__L_CURLY__align__R_CURLY__
\end{align}
</math>
::<math>\approx 9 \times 10^9</math> [[Njuton|N]][[metre|m]]<sup>2</sup>[[Coulomb|C]]<sup>−2</sup> (gjithashtu në metra [[metri|m]][[Farad|F]] <sup>−1</sup>).<ref>[http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefor.html#c3 Coulomb's constant], Hyperphysics</ref>
== Forma vektoriale ==
:<math>\mathbf{Fmathbf__L_CURLY__F} = {1__L_CURLY__1 \over 4\pi\varepsilon_0}{q_1q_2varepsilon_0__R_CURLY____L_CURLY__q_1q_2(\mathbf{r}_1mathbf__L_CURLY__r__R_CURLY___1 - \mathbf{r}_2mathbf__L_CURLY__r__R_CURLY___2) \over |\mathbf{r}_1mathbf__L_CURLY__r__R_CURLY___1 - \mathbf{r}_2mathbf__L_CURLY__r__R_CURLY___2|^3} = {1__L_CURLY__1 \over 4\pi\varepsilon_0}{q_1q_2varepsilon_0__R_CURLY____L_CURLY__q_1q_2 \over r^2}2__R_CURLY__\mathbf{mathbf__L_CURLY__\hat{r}hat__L_CURLY__r}_{21}___L_CURLY__21__R_CURLY__</math>,
=== Sistem me ngarkesa diskrete ===
Parimi i [[mbivendosjes lineare]] mund të përdoret për të llogaritur forcën mbi një thërrmije prove të vogël, <math>\scriptstyle{q}scriptstyle__L_CURLY__q__R_CURLY__</math>, nga një sistem i <math>\scriptstyle{N}scriptstyle__L_CURLY__N__R_CURLY__</math> ngarkesave diskrete :
:<math>\mathbf__L_CURLY__F__R_CURLY__(\mathbf__L_CURLY__r__R_CURLY__) = __L_CURLY__q \over 4\pi\varepsilon_0__R_CURLY__\sum___L_CURLY__i=1__R_CURLY__^N __L_CURLY__q_i(\mathbf__L_CURLY__r}- \mathbf__L_CURLY__r__R_CURLY___i) \over |\mathbf__L_CURLY__r}- \mathbf__L_CURLY__r__R_CURLY___i|^3}= __L_CURLY__q \over 4\pi\varepsilon_0__R_CURLY__\sum___L_CURLY__i=1__R_CURLY__^N __L_CURLY__q_i \over R___L_CURLY__i__R_CURLY__^2__R_CURLY__\mathbf__L_CURLY__\hat__L_CURLY__R}}___L_CURLY__i__R_CURLY__</math>,
:<math>\mathbf{F}(\mathbf{r}) = {q \over 4\pi\varepsilon_0}\sum_{i=1}^N {q_i(\mathbf{r} - \mathbf{r}_i) \over |\mathbf{r} - \mathbf{r}_i|^3} = {q \over 4\pi\varepsilon_0}\sum_{i=1}^N {q_i \over R_{i}^2}\mathbf{\hat{R}}_{i}</math>,
=== Shpërndarja e vazhdueshme e ngarkesës ===
== Tabele e madhësive të derivuara ==
{__L_CURLY__| border="1" style="border-collapse: collapse;" cellpadding="15"
| ||Vetija e thërrmijës||Relacioni||Vetija e fushës
|-
|-
|Madhësi vektoriale||
{__L_CURLY__| border="0"
|''Forca (tek 1 nga 2)''
|-
|<math>\mathbf{F}_{12}mathbf__L_CURLY__F__R_CURLY_____L_CURLY__12__R_CURLY__= {1__L_CURLY__1 \over 4\pi\varepsilon_0}{q_1varepsilon_0__R_CURLY____L_CURLY__q_1 q_2 \over r^2}2__R_CURLY__\mathbf{mathbf__L_CURLY__\hat{rhat__L_CURLY__r}}_{21___L_CURLY__21} \ </math>
|__R_CURLY__
|}
|<math>\mathbf__L_CURLY__F__R_CURLY_____L_CURLY__12__R_CURLY__= q_1 \mathbf__L_CURLY__E__R_CURLY_____L_CURLY__12__R_CURLY__</math>||
|<math>\mathbf{F}_{12}= q_1 \mathbf{E}_{12}</math>||
{__L_CURLY__| border="0"
|''Fusha elektrike (tek 1 nga 2)''
|-
|<math>\mathbf{E}_{12}mathbf__L_CURLY__E__R_CURLY_____L_CURLY__12__R_CURLY__= {1__L_CURLY__1 \over 4\pi\varepsilon_0}{q_2varepsilon_0__R_CURLY____L_CURLY__q_2 \over r^2}2__R_CURLY__\mathbf{mathbf__L_CURLY__\hat{rhat__L_CURLY__r}}_{21___L_CURLY__21} \ </math>
|__R_CURLY__
|}
|-
|Relacioni||<math>\mathbf__L_CURLY__F__R_CURLY_____L_CURLY__12__R_CURLY__=-\mathbf__L_CURLY__\nabla__R_CURLY__U___L_CURLY__12__R_CURLY__</math> || ||<math>\mathbf__L_CURLY__E__R_CURLY_____L_CURLY__12__R_CURLY__=-\mathbf__L_CURLY__\nabla__R_CURLY__V___L_CURLY__12__R_CURLY__</math>
|Relacioni||<math>\mathbf{F}_{12}=-\mathbf{\nabla}U_{12}</math> || ||<math>\mathbf{E}_{12}=-\mathbf{\nabla}V_{12}</math>
|-
|Madhësi skalare||
{__L_CURLY__| border="0"
|''[[Energjia potenciale]] (tek 1 nga 2)''
|-
|<math>U_{12}U___L_CURLY__12__R_CURLY__={1__L_CURLY__1 \over 4\pi\varepsilon_0}{q_1varepsilon_0__R_CURLY____L_CURLY__q_1 q_2 \over r} \ </math>
|__R_CURLY__
|}
|<math>U_{12}U___L_CURLY__12__R_CURLY__=q_1 V_{12V___L_CURLY__12} \ </math>||
{__L_CURLY__| border="0"
|''Potenciali (tek 1 nga 2)''
|-
|<math>V_{12}V___L_CURLY__12__R_CURLY__={1__L_CURLY__1 \over 4\pi\varepsilon_0}{q_2varepsilon_0__R_CURLY____L_CURLY__q_2 \over r} </math>
|__R_CURLY__
|}
|__R_CURLY__
|}
== Shikoni gjithashtu ==
| 