emf is maximum when flux linking the coil is zero

Hi

Could you kindly help me with the query included in the attachment? Please note that at the end of the question it reads, "What does it mean?". Thank you.

Regards
PG

Hi,

EMF depends on the rate of change of flux, not the flux itself. Thus when the rate of change of flux is high, the EMF is high. It doesnt matter that the absolute value of the flux itself is zero or not, as long as it is changing quickly.

Is that what you were wondering?

LATER:
I should have mentioned that for this example the flux is zero when the derivative is max so there is a relationship between the flux and the rate of change of flux, but most important is that the rate of change is not zero and that's how we get the EMF.

Thank you, MrAl.

I'm afraid you didn't understand my confusion. I understand that the induced voltage is directly proportional to rate of change of flux and rate of change of flux is maximum the flux graph is crossing the x-axis. I would request you to have another look **broken link removed**.

In the embedded picture below in "(a)" the flux linking the coil is maximum but the induced voltage is zero, and in "(b)" the flux linking the coil is zero but the induced voltage is maximum. What is this "flux linking the coil"? Thank you.





Regards
PG

Hi PG,


The flux linking the coil is the flux that actually goes through the wires in the coil. The flux is what moves the electrons in the wire because of the motion.
There is flux that doesnt link the coil, and that's the flux that is not penetrating. So if we had a large field and a small coil only part of the field lines would actually go through the coil.

Thank you, MrAl.

Either I have it totally wrong or you aren't getting what I'm asking for. I have a feeling that the latter is true!

In the picture below, do you think there is less flux linking the coil in "(b)" or as, as you say, less flux is penetrating the coil? If you visualize it in three dimensions, you can easily see that more flux is penetrating the coil in "(b)" than in "(a)" but still flux linkage is maximum in "(a)" and zero in "(b)". Let me elaborate it a bit. In "(a)" you have a horizontal wall in path of the flux but in "(b)" you have a vertical wall erected in path of the flux flow. Obviously, the vertical wall provides more obstruction to the flow of flux than the horizontal wall. Now please help me. Thank you.


**broken link removed**



Regards
PG

Hi,


If i understand you correctly, the thing is we have to take the motion of the wire relative to the field into consideration too.
For a small change in angle in (a) the wire at the top of the coil is moving tangent to the B field, or parallel (but in the other direction).
For a small change in angle in (b) the wire at the left side of the coil (which was the top in (a) ) is moving perpendicular to B.
So in B we see the force is perpendicular to B so we get power generation ( the force must be perpendicular to the B field and to the wire).
There are two positions (plus or minus 90 degrees) where the tangential movement is exactly in line with the B field (either against or opposite).
There are two positions (0 or 180 degrees) where the tangential movement is exactly perpendicular to the B field.

The area of the coil presented to the B field has to be more in (a) than in (b) if you consider the coil to be made of only one turn (the simplest case). For a very very thin wire and approximating a field line as being very very thin but not zero, the coil in (b) would have only one set of field lines going through it that does not constitute an area (a square has area, but reduce that square to just one line on one side and it has zero area, a cube has volume, but reduce that to one side only and there is zero volume). So the x,y plane cuts the coil in B, but the y,z plane cuts the coil in (a) (where x is left and right, y is into and out of the page, and z is up and down). The flux lines are passing through any surface in the y,z plane, the coil can be though of as a surface in the y,z plane in (a) and in the x,y plane in (b).

Im not sure if i helped here or not yet