Magnetic flux

Chau

2010-05-27 4:42 am

For a magnetic flux, what is the definition of area?
In a case,a disc rotate inside a solenoid which face the magnetic field.People define that there is an change in area hence it will induce EMF, and the area=pi r^2 x/2pi=r^2 x/2,dA/dt=r^2 w/2.But why we define this as the area?In fact, if we define the disc area,the area is always 2pi r^2.
For a rectangular coil moving toward right, B-field is set to be pointing in the paper, we say there is no induced EMF in this case,since no rate of change in magnet flux. Indeed, if we define the area be the area traveled by the coil, it seems there is changing in area, can we say it induce EMF?

回答 (1)

六呎將軍

2010-05-28 7:55 am

✔ 最佳答案

Indeed, magnetic flux through an area is not applicable for the case of a metal disc owing to its shielding effect.

To derive an expression for induced EMF of a rotating disc, we should refer to the following diagram:

圖片參考：http://i388.photobucket.com/albums/oo325/loyitak1990/May10/CrazyEM2.jpg

That is, we can divide the disc into infinite no. of strip with each spanning from its centre to its edge.

So each strip has a length of R = radius of the disc.

AAlso we can see that the EMF is across the centre and a point on the edge of the disc.

To find the total EMF, we should first give the expression of the EMF induced in the small length segment dx which is :

dV = Bvdx = Bωxdx

So total EMF is found by integrating x from 0 to R:

V = ∫ (x = 0 → R) Bωxdx

= BωR2/2

= B(2πf)R2/2

= Bf(πR2)

= BfA

where f = no. of revolution per sec and A = area

參考: Myself

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