Coefficients of potential について

Words near each other

Dictionary Lists

mini英和辞書

mini和英辞書

翻訳と辞書　辞書検索 [ 開発暫定版 ]

スポンサードリンク

Coefficients of potential ：ウィキペディア英語版

Coefficients of potential

In electrostatics, the coefficients of potential determine the relationship between the charge and electrostatic potential (electrical potential), which is purely geometric:
:

\begin\phi_1 = p_Q_1 + \cdots + p_Q_n \\\phi_2 = p_Q_1 + \cdots + p_Q_n \\\vdots \\\phi_n = p_Q_1 + \cdots + p_Q_n\end.

where ''Q''_i is the surface charge on conductor ''i''. The coefficients of potential are the coefficients ''p''_ij. φ_i should be correctly read as the potential on the i-th conductor, and hence "

p_

" is the p due to charge 1 on conductor 2.
:

p_ =  = \left( \right)_,...,Q_n},

or more formally
:

p_ = \frac\int_\frac{R_{ji}}.

Note that:
# ''p''_ij = ''p''_ji, by symmetry, and
# ''p''_ij is not dependent on the charge,
The physical content of the symmetry is as follows:
: if a charge ''Q'' on conductor j brings conductor i to a potential φ, then the same charge placed on i would bring j to the same potential φ.
:
In general, the coefficients is used when describing system of conductors, such as in the capacitor.
==Theory==

''System of conductors. The electrostatic potential at point P is

\phi_P = \sum_^\frac\int_\frac^\frac\int_\frac,

where ''R''_ji = " TITLE="equipotential surface or the point ''P'' chosen on surface i) contained in a system of conductors j = 1, 2, ..., ''n'':
:

\phi_i = \sum_^\frac\int_\frac,

where ''R''_ji = ">r_i - r_jle\sigma_j\rangle f_j = \fracf_j.
Then,
:

\phi_i = \sum_^n\frac\int_\frac^n p_Q_j \mbox,

i.e.
:

p_ = \frac\int_\frac{R_{ji}}.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
■ウィキペディアで「Coefficients of potential」の詳細全文を読む

スポンサードリンク

翻訳と辞書 : 翻訳のためのインターネットリソース