| English | 意味 |
|---|---|
| magnetic flux/mæɡˈnetɪk flʌks/ | 磁束 |
| webers/ˈveɪbəz/ | ウェーバー |
How much magnetism threads through this loop?
- Hold a wire loop in a magnetic field and count the field lines passing through.
- That "amount of field through the loop" is magnetic flux 磁通量.
- It is the magnetic twin of the electric flux from the Gauss unit.
- And a change in it is what makes generators and transformers work.
Flux is B through an area
- Give the loop an area vector $\vec A$ along its normal.
- The flux is $\Phi_B = \vec B \cdot \vec A = BA\cos\theta$.
- $\theta$ is the angle between the field and the loop's normal.
- Face-on to the field gives maximum flux; edge-on gives zero.
平面ループを通る磁束は:
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
$\Phi_B = \vec B \cdot \vec A = BA\cos\theta$.
$2\ \text{T}$の磁場が $\theta = 0$ $0.3\ \text{m}^2$ のループをまっ通り通過する。磁束を求めよ（単位: Wb）。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
$\Phi_B = BA\cos 0 = 2 \times 0.3 \times 1 = 0.6\ \text{Wb}$.
磁場に対して縁立ち（側面向け）になっているループ（$\theta = 90^\circ$）はゼロ磁束を持つ。
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
$\cos 90^\circ = 0$ なので、$\Phi_B = 0$ 縁立ち。
Three ways to change the flux
- Change the field strength $B$ (move a magnet closer or farther).
- Change the area $A$ the field passes through (stretch or shrink the loop).
- Change the angle $\theta$ (rotate the loop in the field).
- Any of these three changes the flux — and that is what induces an EMF.
ループを通る磁束を変える方法として正しいものをすべて選びよ。
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
磁束の変化はB、A、またはθの変更によって生じる。色には何の関係もない。
Units and varying fields
- Magnetic flux is measured in webers 韦伯 (1 Wb $= 1\ \text{T}\cdot\text{m}^2$).
- For a uniform field and flat loop, just use $\Phi_B = BA\cos\theta$.
- If the field varies across the loop, integrate: $\Phi_B = \int \vec B \cdot d\vec A$.
- A coil of $N$ turns links $N$ times the flux of one loop.
磁束が最大になるのはいつか？
磁束はループが磁場に対してどのように配置されているかに依存する。各ケースを分類せよ。
磁束のSI単位は ____ 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
1 ウェーバー $= 1\ \text{T·m}^2$。
Why flux matters
- On its own, a steady flux does nothing special.
- But a changing flux drives a current in the loop.
- The faster the flux changes, the bigger the effect.
- That link — flux change to induced EMF — is the next lesson.
ループに実際に誘起電動力を生じさせるものは何か？
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
変化しない磁束だけでは誘起電動力は生じない。
A $0.5\ \text{T}$ field passes straight through ($\theta = 0$) a loop of area $0.2\ \text{m}^2$.
- $\Phi_B = BA\cos\theta = 0.5 \times 0.2 \times 1$.
- $\Phi_B = 0.1\ \text{Wb}$.
The angle $\theta$ is measured from the loop's normal, not from its face. A loop lying edge-on to the field ($\theta = 90^\circ$) has zero flux even though the field is strong — a classic angle trap.
Magnetic flux is the field through a loop: $\Phi_B = \vec B \cdot \vec A = BA\cos\theta$ (webers). You can change it by changing $B$, the area $A$, or the angle $\theta$. A changing flux is what induces an EMF — the key to the whole unit.