Questions about eddy currents

[type_writer]

Hey guys, the other day i was reading about eddy currents and it was getting intersting, except i had a few questions going through my mind that i couldn't find answers to and wanted to ask:

say we have a circular bit of aluminium which is our brake disc and an electromagnet which induces the current in the disc;

what would be the effect on the braking force if the circular disc were to be cut into 2 semi circles that weren't touching?

on one hand we still have the same amount of aluminium but I am unsure as to how the induced current flowing through the aluminium would be affected. am i correct in believing that the current induced is proportional to the magnetic field induced and so is proportional to the braking force?

i guess what I am really asking is what is the relationship between the area of the aluminium and the induced currents and how do the two magnetic fields interact.

I haven't properly studied this yet, so please forgive any mistakes.

thanks

 

[cragar]

The current will be proportional to the change in magnetic flux , Faradays law.
And the current will flow in such a way as to oppose the change in B flux lenzs law.
Now that you cut the aluminum ring in half it will make the eddy current change quite a bit.

 

[type_writer]

The current will be proportional to the change in magnetic flux , Faradays law.
And the current will flow in such a way as to oppose the change in B flux lenzs law.
Now that you cut the aluminum ring in half it will make the eddy current change quite a bit.

ok

any ideas what kind of relationship there would be between the area of the aluminium and the eddy currents?

 

[Gordianus]

If you assume the B field is confined to region of diameter D, the eddy currents are important in an area some times D^2. Thus, as long as the disc´s diameter is greater then D, the braking force is the same.
If you have masochistic tendencies,by all means read Smythe's "Static and dynamic electricity", you'll find lots of information about eddy currents.

 

[type_writer]

I think i get it now.

One more question, what kind of relationship do you think there would be between the amount of aluminium (i.e. if you put another brake disc next to the existing one) and the braking force?

i was thinking that there would be more induced current and thus a higher induced field, but would this change be linear?

thanks