Magnetic Flux
Introduced| English |
|---|
| magnetic flux/mæɡˈnetɪk flʌks/ |
| webers/ˈveɪbəz/ |
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.
Magnetic flux through a flat loop is:
$\Phi_B = \vec B \cdot \vec A = BA\cos\theta$.
A $2\ \text{T}$ field passes straight through ($\theta = 0$) a $0.3\ \text{m}^2$ loop. Find the flux (in Wb).
$\Phi_B = BA\cos 0 = 2 \times 0.3 \times 1 = 0.6\ \text{Wb}$.
A loop lying edge-on to the field ($\theta = 90^\circ$) has zero flux.
$\cos 90^\circ = 0$, so $\Phi_B = 0$ edge-on.
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.
Select all the ways to change the flux through a loop.
Flux changes by altering B, A, or θ. Colour has nothing to do with it.
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.
When is the magnetic flux greatest?
Magnetic flux depends on how the loop is oriented in the field. Sort each case.
The SI unit of magnetic flux is the ____.
1 weber $= 1\ \text{T·m}^2$.
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.
What actually induces an EMF in a loop?
Only a changing flux drives an induced EMF.
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.