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Physics · 术语表

什么是 Electric field？

Definition 14.3 High School Physics · 第 14 章 — Electric and Gravitational Fields

If a small test charge $q$ placed at a point $M$ feels an electric force $\vect F$ , the electric field at $M$ is

\vect E = \frac{\vect F}{q} \qquad \text{(in $\mathrm{N}/\mathrm{C}$, also written $\mathrm{V}/\mathrm{m}$)}.

$\vect E$ depends only on the sources and on $M$ , not on the test charge: doubling $q$ doubles $\vect F$ , leaving the quotient unchanged.

示例

Example 14.5 (Reading a field)

A test charge $q = +2.0 \times 10^{-8}\,\mathrm{C}$ at $M$ feels a force of $6.0 \times 10^{-4}\,\mathrm{N}$ pointing east. The field at $M$ is $E = 6.0 \times 10^{-4} / 2.0 \times 10^{-8} = 3.0 \times 10^{4}\,\mathrm{N}/\mathrm{C}$ , pointing east; $q' = -1.0 \times 10^{-8}\,\mathrm{C}$ placed at the same point feels $F = 1.0 \times 10^{-8} \times 3.0 \times 10^{4} = 3.0 \times 10^{-4}\,\mathrm{N}$ — pointing west.

Example 14.7 (A charged sphere)

A Van de Graaff sphere carries $Q = +5.0 \times 10^{-7}\,\mathrm{C}$ (a small charged sphere acts like a point charge at its center). At $d = 0.50\,\mathrm{m}$ :

E = 8.99 \times 10^{9} \times 5.0 \times 10^{-7} / 0.50^2 \approx 1.8 \times 10^{4}\,\mathrm{N}/\mathrm{C},

pointing radially away from the sphere. At $1.0\,\mathrm{m}$ it has dropped to a quarter of this: the $1/d^2$ of the force survives in the field.

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