????? ?????
?????	????? ???????
??????	${\displaystyle F={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}}$
???? ????	???? ??????? ?? ?????
??????	???? ??????? ?? ?????
????? ????? - ?????

??? ?? ????? ?????? ???
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????????? ?????????? ???? ???????? ????? ????? ???? ????? ?????? ?????? ??? ????? ??? ??? ??????? ???? ??????? ???? ???????  / ???? ????? ????? ??????? ????? ???? ?? ???? ??????? ??????? ?????? ?????? ?????? ????????
????????? ??????????? ????? ????? ????? ???? - ?????? ????? ???? ?????????? ??? ???????? ???? ???????? ??? ???????? ?????? ????????? ???? ???????? ????? ????? ??? ????? ????????? ???? ???????? ???? ????? ???? ??????
?????????? ?????????? ??? ?????? ?? ???????????? ????? ??????? ????? ???? ???? ??????? ??????? ??????? ??? ???????????? ???? ????????????? ???? ????????????? ???? ??????? ???? ??????? ???? ??????-?????? ??????? ??????? ???? ????? ??????? ???? ????? ?????? ?????? ??????????????
?????? ?????????? ???? ????? ??? ?????? ???? ????? ???? ??????? ????? ??????? ????? ?????? ????? ??? ??? ????? ???????? ?????? ????? ????? ??? ???? ??????? ?????? ???? ???? ??????? ??? ??????? ???? ????
????? ?????? ???? ???????????? ( ???? ?????-???? ) ???? ????? ??? ????? ????????????
????? ????? ??? ????? ???? ???????? ??????? ???? ???? ??????? ???? ????? ???????? ??????? ??? ??? ?????? ?????? ??????? ?????? ?????? ??? ??????? ????? ????? ????? ????????? ???? ???? ????? ???? ?????? ??????
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????? ????? ? ?? ????? ??????? ?????? ?????? ?? ????? ?????? ??? ??????? ????????? ?????? ??? ???????? ???????? ??????? ? ??? ??? ??? 1785 ?? ??? ????????? ??????? ???? ??????? ?? ????? ???? ?????? ?? ????? ??????? ?????????? ? ?? ????? ????? ?????? ??????? ?????? ?????? ????? ???? ??? ???????? ???????? ??? ???? ??????? ????? ????? ??????? ????? ???? ?????? ????? ??? ??? ?????? ??????? ????????? ???? ???? ???? ????????? ?????.

?? ????? ????? [ ??? ]

≪??? ??????? ?? ??????? ??? ?????? ?? ?????? ?????? ?????? ?? ?????? ??????? ????? ??? ????????? ?????? ?? ???? ??????? ??????≫.

?????? ???????? [ ??? ]

${\displaystyle {\vec {F}}_{12}=k\cdot {\frac {q_{1}\cdot q_{2}}{r_{12}^{2}}}{\frac {{\hat {\vec {r}}}_{12}}{r_{12}}}}$

??? ??:

• ${\displaystyle {\vec {F}}_{12}}$: ?? ????? ????????? ??? ???????? ????? ????? .
• ${\displaystyle q_{1}}$: ???? ?????? ?????? ????? ????? .
• ${\displaystyle q_{2}}$: ???? ?????? ??????? ????? ?????.
• ${\displaystyle {\hat {\vec {r}}}_{12}}$: ???? ?????? ?????? ????? ???? ??????? ?? ?????? ?????? ??? ?????? ???????.
• ${\displaystyle {r_{12}^{2}}}$: ???? ??????? ??? ???????? ????? ??? ?????.

??????? ??? ??????? [ ??? ]

1. ???? ???????? ???? ???? ????? (???? ?????? ??????? ???? ?? ??????? ???? ??????? ???????).
2. ?? ????? ???? ???? ????? ???? ????? ??? ????? ????? ????? (?? ??? ???? ????? ?? ?????) ????? ????? ??? ?? ??? ????.
3. ??????? ??????? ???? ??? ?????? ?????? ??????? ?????? ??????? ??????? ??????.

????? ????? ????? [ ??? ]

1. ????? ?????? ?????? ?? ????? ????????.
2. ????? ?????? ?????? ?? ???? ??????? ??? ????????.

??? ???? ??????? [ ??? ]

???? ????? ?? ????? ????? ?? ???? ???? ??? ????? ?????:

?????? ????? ?????????????? ??? ????? ?? ???? ??????? ?????????? ?????? ????? ?? ???? ??? ????????? ??????? ????? ?? ???? ??????? ??? ????????.

${\displaystyle F=k_{\mathrm {e} }{\frac {q_{1}q_{2}}{r^{2}}}}$

??? r ?? ??????? ??? ????? ?????????

q_1 ???? ?????? 1 ? q_2 ???? ?????? 2?

? k _e ???? ????? .

???? ????? [ ??? ]

k : ?? ???? ????? ????? ????? ?? ????? ??? ???? ??? ????? ?????. ? ?? ??? ???????:

${\displaystyle k={\frac {1}{4\pi \varepsilon _{0}\varepsilon }}}$

????? ????? ??????:

${\displaystyle {\begin{aligned}k_{\mathrm {e} }&={\frac {1}{4\pi \varepsilon _{0}}}={\frac {c^{2}\ \mu _{0}}{4\pi }}=c^{2}\cdot 10^{-7}\ \mathrm {H} \cdot \mathrm {m} ^{-1}\\&=8.987\ 551\ 787\ 368\ 176\ 4\times 10^{9}\ \mathrm {N\cdot m^{2}\cdot C^{-2}} .\\\end{aligned}}}$

???? ??????? ?? ???? ??????? ?????? ???? ????? ?? ?????? ??????? ??? C' _O ' ^[1] ?? 299792458 ??? . ????? ¹ ??????? ?????????? ( μ ₀ )? ??????? ??????? nowrap|4π × 10 ^?7 ?? · ? ?? ???? ??? ????? ?????? ????????? ( ε ₀ ) ??????? ε ₀ = 1/( μ ₀
c ²
₀ ) ? 8.854 187 817 × 10 ^?12   ? · ? ^?1 .?? ????? cgs? ???? ??????? esu of charge ?? ???? ????? statcoulomb? ??????? ???? ?? ??? ???? ????? ≪?????≫ ???? ????? 1.

?????? ??????? [ ??? ]

???? ??? ????? ??? ?????? ??? ????? ?????? ????????? ( E ) ???? ????? ???? ????? ????? ( q ) ??? ????? ????? ( r ) ??:

${\displaystyle E={1 \over 4\pi \varepsilon _{0}}{\frac {q}{r^{2}}}.}$

?????? ??? ???? ?????? ???? ??????? ?? ?????? ??? ??? ???? ????? ????????? ?????? ?????? ?? ???? ?????? ???????? ?? ??? ?? ??????? ?? ??? ?????? ?????? ????? SI ?????? ??????? ?? ???? ??? ??? ?? ????? ?? ???????.

??? ????? [ ??? ]

?????? ???? ????? ?????? ????? ???????? (?????????):

???? ????? ???? ?????? ?? ??????:

${\displaystyle {\begin{aligned}k_{e}&={\frac {1}{4\pi \varepsilon _{0}}}\end{aligned}}}$

???: : ${\displaystyle {\begin{aligned}\varepsilon _{0}\end{aligned}}}$ ?????? ?????? ????????

??????? ?????? ????? ??????:

${\displaystyle |{\boldsymbol {F}}|=k_{e}{|q_{1}q_{2}| \over r^{2}}}$.

??? ?????  :

${\displaystyle U_{E}(r)=k_{e}{\frac {qQ}{r}}}$.

???:

q ?????? ????????

Q ?????? ????????

?????? ??? ????? ????????? ?????? ?????? ???? ?????? ?????? ???? ???? ????? ??????? (???? ??? ?????????? .

????? ?????? ??????? [ ??? ]

?????? ????? ??? ????? ??? ??????? ???????? ??? ?????? ????? ????? ???????? ????? ?? ???? ?????? ????? ?? ?????? ????? ????? ${\displaystyle dq}$.

?????? ??? ????? (??? ????? ??? ????? ?? ???) ??? ${\displaystyle \lambda (\mathbf {r^{\prime }} )}$ ???? ?????? ????? ??? ??? ?????? ${\displaystyle \mathbf {r^{\prime }} }$? ? ${\displaystyle dl^{\prime }}$ ?? ???? ??? ?????? ??????

${\displaystyle dq=\lambda (\mathbf {r^{\prime }} )dl^{\prime }}$.

?????? ???? ????? (??? ????? ??? ????? ?? ??? ??? ( ???? ) ??? ??? ?????) ??? ${\displaystyle \sigma (\mathbf {r^{\prime }} )}$ ???? ?????? ????? ??????? ??? ?????? ${\displaystyle \mathbf {r^{\prime }} }$, and ${\displaystyle dA^{\prime }}$ ?? ???? ????? ?????? ??????

${\displaystyle dq=\sigma (\mathbf {r^{\prime }} )\,dA^{\prime }.\,}$

?????? ???? ????? (????? ?? ????? ????? ???? ???? ??????) ??? ${\displaystyle \rho (\mathbf {r^{\prime }} )}$ ???? ?????? ????? ????? ??? ?????? ${\displaystyle \mathbf {r^{\prime }} }$? ? ${\displaystyle dV^{\prime }}$ ?? ???? ??? ?????? ??????

${\displaystyle dq=\rho (\mathbf {r^{\prime }} )\,dV^{\prime }.}$

????? ??? ???? ?????? ????? ${\displaystyle q^{\prime }}$ ??? ?????? ${\displaystyle \mathbf {r} }$ ??

${\displaystyle \mathbf {F} =q^{\prime }\int dq{\mathbf {r} -\mathbf {r^{\prime }} \over |\mathbf {r} -\mathbf {r^{\prime }} |^{3}}.}$

??????? ???????? [ ??? ]

??? ???? ???????? ????????? ?????? ????? ????? ????????? ?????? ????? ???? ???? ???????? ???????? ?????? ???? ????? ?????.

???? ????? ?? ???? ??????? ?????? ????? ?? ????? ??????? ?? ???? ?? ???? ???? ?????? ????? ?? ???? ??? ??????? ?????? ??? ???? ?????? ??? ????? ??????? ????? ?????? ??? ???? ????? ??????? ??? ?? ????. ????? ???? ??? ???? ???? ????? ????? ??????? ?? ????? ??????? ?? ????? ????.

??????? ??????? ??????? ?????? ???? ???? ?????? ??????? ?????? ???? ??????? ?? ???????? ?? ???? ??????? ???? ????????? ???????.

???? ??????? ??????? [ ??? ]

	????? ??????	???????	????? ??????
?? ??????	????? (??? 1 ?? 2) ${\displaystyle \mathbf {F} _{12}={1 \over 4\pi \varepsilon _{0}}{q_{1}q_{2} \over r^{2}}\mathbf {\hat {r}} _{21}\ }$	${\displaystyle \mathbf {F} _{12}=q_{1}\mathbf {E} _{12}}$	???? ??????? (??? 1 ?? 2) ${\displaystyle \mathbf {E} _{12}={1 \over 4\pi \varepsilon _{0}}{q_{2} \over r^{2}}\mathbf {\hat {r}} _{21}\ }$
???????	${\displaystyle \mathbf {F} _{12}=-\mathbf {\nabla } U_{12}}$		${\displaystyle \mathbf {E} _{12}=-\mathbf {\nabla } V_{12}}$
???? ?????	???? ????? (??? 1 ?? 2) ${\displaystyle U_{12}={1 \over 4\pi \varepsilon _{0}}{q_{1}q_{2} \over r}\ }$	${\displaystyle U_{12}=q_{1}V_{12}\ }$	????? (??? 1 ?? 2) ${\displaystyle V_{12}={1 \over 4\pi \varepsilon _{0}}{q_{2} \over r}}$

????? [ ??? ]

?? ????? ??? ?????? ??: ????? ?????

• ????? ??????????
• ????? ????????
• ????? ?????