| English | 意味 |
|---|---|
| field/fiːld/ | 場 |
| electric field/ɪˈlektrɪk fiːld/ | 電場 |
| test charge/test tʃɑːdʒ/ | 試験電荷 |
| uniform/ˈjuːnɪfɔːm/ | 均一な |
How does one charge feel another across empty space?
- A charge pushes another far away, with nothing visibly between them.
- We explain it with a field 场: charge fills the space around it with influence.
- Any other charge placed there feels a force from the local field.
- The field is the middle-man that carries the electric force.
Field = force per unit charge
- The electric field 电场 at a point is the force a $+1\ \text{C}$ test charge 检验电荷 would feel there.
- $\vec E = \dfrac{\vec F}{q}$, measured in newtons per coulomb (N/C).
- $E$ is a vector: it has a direction at every point.
- Once you know $E$, the force on any charge is just $\vec F = q\vec E$.
ある点における電界とは：
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
$\vec E = \vec F / q$ — 単位正電荷が感じる力である。
場$E$を知れば、電荷$q$にかかる力は$F =$ ____である。
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
$\vec F = q\vec E$—場に電荷を掛け合わせる。
The field of a point charge
- A point charge $Q$ makes a field $E = \dfrac{kQ}{r^2}$ at distance $r$.
- It points away from a positive $Q$ and toward a negative $Q$.
- It is strongest near the charge and fades as $1/r^2$.
- Field lines show the direction; where they crowd, the field is stronger.
電荷の場を描く
電荷の符号と大きさを変えて、場の線がどのように再配置されるか見よう。
$3\ \text{m}$から$+6\ \text{nC}$の電荷による場（N/C単位）を求めよ。$k = 9\times10^9$を使用せよ。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
$E = \dfrac{(9\times10^9)(6\times10^{-9})}{3^2} = \dfrac{54}{9} = 6\ \text{N/C}$.
Reading field lines
- Lines start on positive charge and end on negative charge.
- They never cross — the field has one direction at each point.
- Closer lines mean a stronger field.
- The line's tangent gives the direction of $\vec E$ (and the force on a $+$ charge).
2つの電界線は点で交差することがある。
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
線は決して交差しない—各点で場はただ1つの方向を持つ。
電界線に関する真の記述をすべて選択せよ。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
線は＋から−へ走り、強い箇所で密集し、決して交差しない。
A uniform field
- Between two large parallel plates the field is uniform 均匀 — same everywhere.
- The lines are straight, evenly spaced, and point from $+$ to $-$.
- A uniform field gives a constant force, so a charge moves like a projectile.
- We will use this constant-field picture for capacitors.
2つの大きな平行板の間で場は：
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
平行板は均一な場を作る—直線で、等間隔の線。
Find the field $2\ \text{cm}$ from a $+5\ \text{nC}$ charge. Use $k = 9\times10^9$.
- $E = \dfrac{kQ}{r^2} = \dfrac{(9\times10^9)(5\times10^{-9})}{(0.02)^2}$.
- $E \approx 1.1\times10^{5}\ \text{N/C}$, pointing away from the charge.
The field $\vec E$ exists whether or not a test charge is there — it is a property of space made by the source charge. Don't say "no charge, no field": the source still fills space with $E$.
The electric field is the force per unit charge, $\vec E = \vec F / q$ (N/C), a vector pointing away from $+$ and toward $-$. A point charge makes $E = kQ/r^2$; field lines show its direction, and closer lines mean a stronger field.