庫侖定律

發現過程及地位

1767年，英格蘭化學家約瑟夫·普利斯特里猜測電荷之間的交互作用力具有類似於萬有引力的平方反比形式。[1][2]

1769年，蘇格蘭物理學家約翰·羅比遜首次通過實驗發現兩個帶電球體之間的作用力與它們之間距離的2.06次方成反比。[3]

1770年代早期，著名英國物理學家亨利·卡文迪什通過巧妙的實驗，得出了帶電體之間的作用力依賴於帶電量與距離，並得出靜電力與距離的 $2 \pm \frac{1}{50}$ 次方成反比，只是卡文迪什沒有公布這個結果。[4]

純量形式

$F = k_{\mathrm{e}}\frac{qq'}{r^2}$

\begin{align} k_{\mathrm{e}} &= \frac{1}{4\pi\epsilon_0} \\ &= 8.987\ \times 10^9 \ \mathrm{N \cdot m^2 \cdot C^{-2}} \\ \end{align}

向量形式

$\mathbf{F}= \cfrac{1}{4\pi\epsilon_0}\cfrac{qq'\ (\mathbf{r} - \mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|^3}$

電場

$\mathbf{F} =q[\mathbf{E}+\mathbf{v}\times\mathbf{B}]$

$\mathbf{v} =0$

$\mathbf{F} =q\mathbf{E}$

$\mathbf{E}= {1 \over 4\pi\epsilon_0}\frac{q'\ (\mathbf{r} - \mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|^3}$

離散電荷系統

$N$ 個點電荷所組成的一個系統，其作用於一個電量為 $q$ ，位置為 $\mathbf{r}$ 的檢驗電荷的靜電力，可以用疊加原理來計算：

$\mathbf{F}= \cfrac{q}{4\pi\epsilon_0}\sum_{i=1}^N \cfrac{q_i'\ (\mathbf{r} - \mathbf{r}_i')}{|\mathbf{r} - \mathbf{r}_i'|^3}$

連續電荷分佈

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

$dq' = \sigma(\mathbf{r^\prime})da^\prime$

$dq' = \rho(\mathbf{r^\prime})d\tau^\prime$

$\mathbf{F}(\mathbf{r}) =q\int dq'\ \frac{\mathbf{r} - \mathbf{r}^\prime}{|\mathbf{r} - \mathbf{r}^\prime|^3}$

物理量表格

$\mathbf{F}= {1 \over 4\pi\epsilon_0}\cfrac{q q'\ (\mathbf{r} - \mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|^3}$
$\mathbf{F}= q \mathbf{E}$

$\mathbf{E}= {1 \over 4\pi\epsilon_0}\cfrac{q'\ (\mathbf{r} - \mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|^3}$

$U={1 \over 4\pi\epsilon_0}{q q' \over |\mathbf{r} - \mathbf{r}'|}$
$U=q V$

$V={1 \over 4\pi\epsilon_0}{q' \over (|\mathbf{r} - \mathbf{r}'|)}$

參考文獻

1. ^ Joseph Priestley, The History and Present State of Electricity, with Original Experiments (London, England: 1767), page 732:

May we not infer from this experiment, that the attraction of electricity is subject to the same laws with that of gravitation, and is therefore according to the squares of the distances; since it is easily demonstrated, that were the earth in the form of a shell, a body in the inside of it would not be attracted to one side more than another?

2. ^ Robert S. Elliott. Electromagnetics: History, Theory, and Applications. 1999. ISBN 978-0-7803-5384-8
3. ^ John Robison, A System of Mechanical Philosophy (London, England: John Murray, 1822), vol. 4. On page 68, the author states that in 1769 he announced his findings regarding the force between spheres of like charge. On page 73, the author states the force between spheres of like charge varies as x-2.06.
4. ^ 4.0 4.1 James Maxwell, ed., The Electrical Researches of the Honourable Henry Cavendish... (Cambridge, England: Cambridge University Press, 1879), pages 104-113: "Experiments on Electricity: Experimental determination of the law of electric force."
5. ^ Williams, E. R.; J. E. Faller, H. A. Hill, New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass, Physics Review Letters. 1971, 26 (12): 721-724, doi:10.1103/PhysRevLett.26.721
6. ^ 6.0 6.1 *喬治亞州州立大學Georgia State University）線上物理網頁：庫侖常數
7. ^ 美國國家標準與科技研究所網頁：真空電容率
8. ^ Williams, Faller, Hill, New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass, 物理報導期刊. 1971, 26: 721–724
• Griffiths, David J. Introduction to Electrodynamics (3rd ed.). Prentice Hall. 1998. ISBN 0-13-805326-X. * Tipler, Paul. Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. 2004. ISBN 0-7167-0810-8.