| English | 意味 |
|---|---|
| magnetic flux density/mæɡˈnetɪk flʌks ˈdensɪti/ | 磁束密度 |
| Fleming's left-hand rule/ˈflemɪŋz left hænd ruːl/ | フレミングの左手の法則 |
| tesla/ˈteslə/ | テスラ |
The definition hiding inside a motor
- A wire carrying a current across a magnetic field jumps sideways. Every electric motor ever built is that jump, arranged to keep repeating.
- Look at the force closely and something else falls out of it. Nobody can measure a magnetic field directly, but this force can be measured, and it is proportional to $B$.
- So the motor effect is not only an application; it is how the strength of a magnetic field is defined.
- This lesson is $F = BIL\sin\theta$, the definition of magnetic flux density 磁通密度, and Fleming's left-hand rule 弗莱明左手定则.
The force on a current-carrying wire
- A wire of length $L$ carrying current $I$ at angle $\theta$ to a field of flux density $B$ feels a force:
- The force is largest at right angles, where $\sin\theta = 1$ and $F = BIL$, and zero when the wire lies along the field, where $\sin\theta = 0$.
- The force is at right angles to both the current and the field, which is why a motor turns rather than pulling itself apart.
磁場中の電流を流す導線にかかる力は：
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
導線が磁場に対して垂直なときに最大（$\sin 90^{\circ} = 1$なので $F = BIL$）。
導線が磁場の方向に沿って置かれると、力ゼロとなる。
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
導線が磁場と平行の場合、$\theta = 0$かつ$\sin\theta = 0$なので、力は生じない。
$0.10\ \text{m}$ 導線に $2.0\ \text{A}$ が $0.50\ \text{T}$ 磁束密度方向と直角に流れている。力はいくらか？
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
$F = BIL = 0.50 \times 2.0 \times 0.10 = 0.10\ \text{N}$.
Magnetic flux density
- Rearranged for a wire at right angles, the same equation defines $B$:
- Magnetic flux density is the force per unit current per unit length on a wire at right angles to the field.
- Its unit is the tesla 特斯拉: $1\ \text{T} = 1\ \text{N/(A m)}$. One tesla is a strong field; the Earth's is about 50 microtesla.
磁束密度は ____ で測定される。
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
$1\ \text{T} = 1\ \dfrac{\text{N}}{\text{A}\cdot\text{m}}$ ——単位電流・単位長さあたりの力である。
磁束密度とは何か？
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
垂直な導線については B = F/(IL) で、単位はテスラ。この定義はモーター効果の力式そのものであり、これがBの測定方法である。
Fleming's left-hand rule
- Hold the thumb and first two fingers of your left hand mutually at right angles.
- First finger is the Field, seCond finger is the Current, thuMb is the force, or Motion.
- Left hand for the motor effect, where a current produces motion. The right hand is for the generator effect, where motion produces a current, and mixing them up reverses every answer.
Three quantities, three directions, all mutually perpendicular
導線にかかる力を体感する
磁場中を流れる電流には、両方に垂直な方向に力 F = BIL が働く——電流を逆転させたり磁石を反転させたりすると、力は反対方向に跳ね返る。
フレミングの左手則において、親指は次のうちどれを示すか：
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
第一指＝磁場、第二指＝電流、親指＝力/運動。
フレミングの左手則の各指と、それぞれが表すものを結びつけてください。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
First-Field, seCond-Current, thuMb-Motion。左手はモーター効果用、右手はジェネレーター効果用である。
Worked example: force on a wire
- A wire of length $0.10\ \text{m}$ carries $2.0\ \text{A}$ at right angles to a field of flux density $0.25\ \text{T}$. Find the force, and then the force if the wire is turned to $30°$ to the field.
- At right angles: $F = BIL = (0.25)(2.0)(0.10) = 0.050\ \text{N}$.
- At $30°$: $F = BIL\sin 30° = 0.050 \times 0.5 = 0.025\ \text{N}$, half as much.
- If the wire were turned parallel to the field the force would be zero. The angle is measured between the wire and the field, not between the wire and anything else.
0.10 m の導線に 2.0 A が 30 度の角度で 0.25 T の磁束密度中を流れている。この導線にかかる力（ニュートン）はいくらか？
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
F = BIL sin30 = 0.25 × 2.0 × 0.10 × 0.5 = 0.025 N。垂直な場合の半分である。磁場に平行なら力はゼロだった。
Two parallel currents
- Each wire sits in the other's field, so each feels a force. Apply the left-hand rule twice and the result is symmetric.
- Currents in the same direction attract. Currents in opposite directions repel.
- This is worth remembering because it is the reverse of what charges do: like charges repel, but like currents attract.
同じ方向に電流を流す2本の平行導線は互いに引き合う。
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
各導線は相手の磁場の中にあり、左手則を適用すれば引き合うことが分かる。これは同種電荷が互いに反発することとは逆である。
Worked example: measuring a field
- A stiff wire on a top-pan balance carries a current through a magnetic field. Explain how this measures $B$.
- The wire is placed at right angles to the field, so the force is $F = BIL$.
- The magnet sits on the balance, and by Newton's third law the force on the magnet is equal and opposite to the force on the wire, so the balance reading changes by $F/g$ in kilograms.
- Then $B = F/(IL)$, using the measured force, the current from an ammeter and the length of wire actually in the field.
- The last detail is the one that catches people: $L$ is the length inside the field, not the whole wire.
電流天秤を用いて磁束密度を測定する手順を正しい順序で並べ替えてください。
難易度 3/5 · 200 コイン + 今日初回完了時に小ボーナス付与
ニュートンの第三法則により、天秤が導線にかかる力に対する反作用を感じることができる。L は磁場内にある部分の長さであり、導線全体の長さではない。
Marks that slip away
- $\theta$ is the angle between the wire and the field. The force is zero when they are parallel, not maximum.
- $L$ is the length of wire in the field.
- Left hand for the motor effect, right hand for the generator effect. Say which you are using.
- Parallel currents in the same direction attract, which is the opposite of like charges.
You've got it
- $F = BIL\sin\theta$: maximum at right angles, zero along the field, and the force is perpendicular to both current and field
- rearranged, it defines magnetic flux density: the force per unit current per unit length on a wire at right angles, in tesla
- Fleming's left-hand rule: First finger Field, seCond finger Current, thuMb Motion, for the motor effect
- parallel currents attract when in the same direction and repel when opposite