Magnetic Flux · 磁通量
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| magnetic flux/mæɡˈnetɪk flʌks/ | 磁通量 | cí tōng liàng |
| webers/ˈveɪbəz/ | 韦伯 | wéi bó |
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.
有多少磁场穿过这个回路?
- 把一个导线回路放在磁场中,数一数穿过它的磁感线。
- 那个"穿过回路的场的量"就是磁通量。
- 它是高斯单元里电通量的磁学孪生。
- 而它的变化正是让发电机和变压器工作的东西。
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.
通量是穿过面积的 B
- 给回路一个沿它法线的面积矢量 $\vec A$。
- 通量是 $\Phi_B = \vec B \cdot \vec A = BA\cos\theta$。
- $\theta$ 是场与回路法线之间的夹角。
- 正对场给出最大通量;侧对给出零。
Magnetic flux through a flat loop is: · 通过平面的磁通量为：
$\Phi_B = \vec B \cdot \vec A = BA\cos\theta$.
A $2\ \text{T}$ field passes straight through ($\theta = 0$) a $0.3\ \text{m}^2$ loop. Find the flux (in Wb). · 一个$2\ \text{T}$场垂直穿过（$\theta = 0$）一个$0.3\ \text{m}^2$回路。求磁通量（单位Wb）。
$\Phi_B = BA\cos 0 = 2 \times 0.3 \times 1 = 0.6\ \text{Wb}$.
A loop lying edge-on to the field ($\theta = 90^\circ$) has zero flux. · 边缘对着场放置的回路（$\theta = 90^\circ$）磁通量为零。
$\cos 90^\circ = 0$, so $\Phi_B = 0$ edge-on. · $\cos 90^\circ = 0$，因此$\Phi_B = 0$边缘对着场。
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.
改变通量的三种方式
- 改变场强 $B$(把磁体移近或移远)。
- 改变场穿过的面积 $A$(拉伸或缩小回路)。
- 改变角度 $\theta$(在场中旋转回路)。
- 这三者中任何一个都改变通量——而这正是感应出电动势的原因。
Select all · 所有 the ways to change the flux through a loop. · 选择改变回路磁通量的所有方法。
Flux changes by altering B, A, or θ. Colour has nothing to do with it. · 磁通量通过改变B、A或θ来变化。颜色与此无关。
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.
单位与变化的场
- 磁通量以韦伯量度(1 Wb $= 1\ \text{T}\cdot\text{m}^2$)。
- 对均匀场和平面回路,只用 $\Phi_B = BA\cos\theta$。
- 若场在回路上变化,就积分:$\Phi_B = \int \vec B \cdot d\vec A$。
- 一个 $N$ 匝的线圈链接一个回路通量的 $N$ 倍。
When is the magnetic flux greatest? · 何时磁通量最大？
Magnetic flux depends on how the loop is oriented in the field. Sort each case. · 磁通量取决于回路在场中的取向。对每种情况进行分类。
The SI unit of magnetic flux is the . · 磁通量的SI单位是。
1 weber $= 1\ \text{T·m}^2$. · 1韦伯$= 1\ \text{T·m}^2$。
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.
为什么通量重要
- 单独来看,稳定的通量没什么特别。
- 但变化的通量会在回路中驱动电流。
- 通量变化得越快,效果越大。
- 那个联系——通量变化到感应电动势——就是下一课。
What actually induces an EMF in a loop? · 什么实际上会在回路中感应出电动势？
Only a changing flux drives an induced EMF. · 只有变化的磁通量才能驱动感应电动势。
A $0.5\ \text{T}$ field passes straight through ($\theta = 0$) a loop of area $0.2\ \text{m}^2$.
- $\Phi_B = BA\cos\theta = 0.5 \times 0.2 \times 1$.
- $\Phi_B = 0.1\ \text{Wb}$.
一个 $0.5\ \text{T}$ 的场垂直穿过($\theta = 0$)一个面积 $0.2\ \text{m}^2$ 的回路。
- $\Phi_B = BA\cos\theta = 0.5 \times 0.2 \times 1$。
- $\Phi_B = 0.1\ \text{Wb}$。
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.
角 $\theta$ 是从回路的法线量起的,不是从它的面。侧对场($\theta = 90^\circ$)的回路通量为零,尽管场很强——一个经典的角度陷阱。
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.
磁通量是穿过回路的场:$\Phi_B = \vec B \cdot \vec A = BA\cos\theta$(韦伯)。你可以通过改变 $B$、面积 $A$ 或角度 $\theta$ 来改变它。变化的通量正是感应出电动势的原因——整个单元的关键。