Electric field inside a charged ring

In summary, the conversation revolves around a problem that involves a charged ring and cuts being made to it. There is a discussion about the stability of the configuration and the resulting electric field at the center. It is suggested that the field at the center is zero due to symmetry, but there are concerns about lurking singularities. The conversation ends with a request for the official answer to the problem.
  • #1
takelight2
12
1
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
circle.PNG
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.
 
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  • #2
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?
 
  • #3
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?
 
  • #4
hutchphd said:
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?
 
  • #5
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.
 
  • #6
@hutchphd - ok, thanks.
@takelight2 - would be very interested to hear the 'official' answer when you have it.
 
  • Like
Likes hutchphd

1. What is the formula for calculating the electric field inside a charged ring?

The formula for calculating the electric field inside a charged ring is E = kQz/(z^2 + R^2)^(3/2), where E is the electric field, k is the Coulomb constant, Q is the total charge of the ring, z is the distance from the center of the ring to the point where the electric field is being measured, and R is the radius of the ring.

2. How does the electric field inside a charged ring vary with distance from the center?

The electric field inside a charged ring varies inversely with the distance from the center of the ring. This means that as the distance from the center increases, the electric field decreases.

3. What is the direction of the electric field inside a charged ring?

The electric field inside a charged ring points towards the center of the ring. This is because the electric field is created by the charges on the ring, which are all attracting towards the center.

4. Can the electric field inside a charged ring ever be zero?

Yes, the electric field inside a charged ring can be zero at the center of the ring. This is because all of the charges on the ring are symmetrically distributed around the center, resulting in a cancellation of the electric field at that point.

5. How does the electric field inside a charged ring change if the ring is made of a different material?

The electric field inside a charged ring is not affected by the material of the ring. It only depends on the total charge and the distance from the center of the ring, as given by the formula E = kQz/(z^2 + R^2)^(3/2).

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