Electric field inside a charged ring

[takelight2]

Homework Statement

What is the direction of the electric field at the centerpoint P of a charged ring when two pieces are cut off to create respective gaps on the rings circumference as shown in the image?

Relevant Equations

E = Kq/r^2

I am just a bit confused here. Would doing this even change the electric field direction at the center at all? I'm thinking no, but a bit of direction would be appreciated. This problem is really simple, I'm just a bit confused.

 

[Steve4Physics]

Are you sure the question is complete/correct?
Is the ring uniformly charged?
What do you think we can say about the field at the centre before and after the cuts?

 

[hutchphd]

The problem is pretty artificial, although that doesn't make it bad. The issue as I see it is that this configuration in 3D is riotously unstable for +or- charge at the center. It will be slightly more unstable with the cuts! Anyone have a more anodyne solution?

 

[Steve4Physics]

The problem is pretty artificial, although that doesn't make it bad. The issue as I see it is that this configuration in 3D is riotously unstable for +or- charge at the center. It will be slightly more unstable with the cuts! Anyone have a more anodyne solution?

Surely the field at the centre is zero both before and after the cuts (due to symmetry). Therefore it makes no sense to ask about the field's direction at the centre. What am I missing?

 

[hutchphd]

I was pointing to conceptual difficulties from lurking singularities, and trying not to provide the answer.(it being homework). I see nothing incorrect in what you said.

 

[Steve4Physics]

@hutchphd - ok, thanks.
@takelight2 - would be very interested to hear the 'official' answer when you have it.