Voltage between centre and edge of conducting disk

[cromata]

Homework Statement

A metal disc of radius R rotates with a constant velocity ω about its axis. FInd the potential difference between the centre and the rim of the disc if:
a)the external magnetic field is absent
b)the external magnetic field of induction B is directed perpendicular to the disc
c)Why is there a difference between results in those two cases if rotE=0 for consant magnetic field (3rd Maxwell equation).

Homework Equations

Δφ=∫Edr
Fmag=qv×B

The Attempt at a Solution

a)Free electrons of metal disc are rotating, so there has to be some force that is responsible for centripetal acceleration of electrons. That force exists because free electrons go to the rim of the disc and create electric field, so we have: Fcp=e*E, E=m*ω^2*r/e. So potential diference is Δφ=∫Edr (from 0 to R), Δφ=mω^2*r^2/2e.
b)I think this question is undefined because it's not same if B and ω are parallel or antiparallel. Let's suppose that they are parallel, then magnetic force on electron is F=Beωr (directed to the centre of the disc), so we have Fcp=B+E, and from here we can calculate E and then use Δφ=∫Edr... but i think i got something wrong in this b)part and i don't know the answer on last question

 

[cnh1995]

a)Free electrons of metal disc are rotating, so there has to be some force that is responsible for centripetal acceleration of electrons. That force exists because free electrons go to the rim of the disc and create electric field, so we have: Fcp=e*E, E=m*ω^2*r/e. So potential diference is Δφ=∫Edr (from 0 to R), Δφ=mω^2*r^2/2e.

There is no magnetic field. How can electrons go to the rim of the disc?

b)I think this question is undefined because it's not same if B and ω are parallel or antiparallel. Let's suppose that they are parallel, then magnetic force on electron is F=Beωr (directed to the centre of the disc), so we have Fcp=B+E, and from here we can calculate E and then use Δφ=∫Edr... but i think i got something wrong in this b)part and i don't know the answer on last question

Have a read.
https://www.google.co.in/url?sa=t&s...QIHDAA&usg=AFQjCNH9N69CnzBKuK7WS0vocM10Eop1Uw

 

[cromata]

Thx, but what is causing potential difference/electric field in a) if electrons don't go to the edge of the rim?

 

[cnh1995]

Thx, but what is causing potential difference/electric field in a) if electrons don't go to the edge of the rim?

There is no potential difference.

 

[cromata]

This problem is from I.E.Irodov: Problems in general physics, and solution in a) says the same thing that i said

 

[cnh1995]

I understood Irodov's solution but I am not sure I can comment on it.

I request @TSny to take a look.
Edit: I see TSny has been offline for a long time.
@gneill, could you please comment on this?

I have some strange feeling about this question..

 

[TSny]

b)I think this question is undefined because it's not same if B and ω are parallel or antiparallel. Let's suppose that they are parallel, then magnetic force on electron is F=Beωr (directed to the centre of the disc), so we have Fcp=B+E, and from here we can calculate E and then use Δφ=∫Edr... but i think i got something wrong in this b)part

I'm not quite sure what your specific question is here. Perhaps you can rephrase it?
In any realistic experimental setup, the centripetal force on an electron is negligible compared to the magnetic force when you have a moderate B field present. So, you may neglect the centripetal force in part (b).

and i don't know the answer on last question

I'm sot sure what question (c) is getting at. It is true that rotE is zero for parts (a) and (b). But I don't see why that would make anyone think that the emf's for (a) and (b) should be the same.

 

[cromata]

-I think that c) part was there just to confuse, (because when you have non-static field you can obtain different potential differences between same two points if you choose 2 diferent paths to go from one point to another. ,you can see in this video from 35th minute what I mean) but a) and b) are two separated situations so c) question actually makes no sense.
-and thanks for part b). So I can just use Ee=Bev and calculate E and Δφ (because Fcp is negliglbe)?

 

[TSny]

-I think that c) part was there just to confuse, (because when you have non-static field you can obtain different potential differences between same two points if you choose 2 diferent paths to go from one point to another. ,you can see in this video from 35th minute what I mean)

Yes, the video is very interesting. Lewin's demo shows how nonconservative E fields can produce nonintuitive results for volt meter readings in circuits.

but a) and b) are two separated situations so c) question actually makes no sense.

Right. The E field is conservative in (a) and (b). But they are, nevertheless, different situations

-and thanks for part b). So I can just use Ee=Bev and calculate E and Δφ (because Fcp is negliglbe)?

Yes, I believe so.