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Physics · 术语表

什么是 Electric dipole？

Definition 27.6 University Physics — Year 1 · 第 27 章 — Electric Potential; Conductors and Capacitors

Two opposite charges $-q$ at $N$ and $+q$ at $P$ , a distance $a = NP$ apart, form an electric dipole of dipole moment $\vect p = q\,\vect{NP}$ ( $\mathrm{C}\,\mathrm{m}$ ), pointing from $-$ to $+$ . The dipole approximation is the study of its field at distances $r \gg a$ . A molecule whose centres of positive and negative charge do not coincide (water, $p = 6.2 \times 10^{-30}\,\mathrm{C}\,\mathrm{m}$ ) is a dipole; a neutral atom in a field becomes one (induced dipole).

Left: the geometry of the dipole approximation — M seen from the centre O at distance r and angle from p, with the radial and orthoradial field components. Right: field lines (blue, r 2) and equipotentials (orange, r √| |) of a dipole pointing right; the plane through O perpendicular to p is the equipotential V = 0. — Left: the geometry of the dipole approximation — $M$ seen from the centre $O$ at distance $r$ and angle $\theta$ from $\vect p$ , with the radial and orthoradial field components. Right: field lines (blue, $r \propto \sin^2\theta$ ) and equipotentials (orange, $r \propto \sqrt{|\cos\theta|}$ ) of a dipole pointing right; the plane through $O$ perpendicular to $\vect p$ is the equipotential $V = 0$ .

示例

Example 27.9 (Why the comb attracts the paper)

A charged comb creates a field that falls off with distance; a scrap of paper, neutral, is polarized by it (induced dipole along $\vect E$ ), and the force $p\,\dd E/\dd x$ on an aligned dipole pulls it toward the strong-field region: the comb. Sign of the comb’s charge irrelevant; the same mechanism holds the balloon on the wall and makes the water stream bend. For water molecules, $pE$ in a $1\,\mathrm{MV}/\mathrm{m}$ field is $6 \times 10^{-24}\,\mathrm{J}$ , $600$ times less than $k_BT$ at room temperature: only a slight net alignment survives the thermal tumbling (Exercise 27.7).

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