Fields inside charged rings vs spherical shells

In summary, the electric field inside a shell of charge is different than the electric field inside a single ring because the fields inside the ring cancel out, while the fields inside the shell don't cancel out.
  • #1
Andrew Wright
120
19
Hi.

Since you can construct shells from a series of rings, why would there be an electric field inside a single ring but not inside a shell?
 
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  • #2
I can construct a shell of charge from a large number of point sources. By your logic doesn’t that mean a point source shouldn’t have a field? In short, your logic is flawed.

Now try to think of it in terms of force vectors. In the plane of the ring all of the force vectors from every piece of the ring lie in the plane of the ring. I won’t bother trying to describe why they add up to zero, but I’ll just state that here they DO cancel. However, if you move out of the plane, now every single force vector has a component perpendicular to the ring WHICH ALL POINT THE SAME DIRECTION. There is nothing to cancel the force in the axis perpendicular to the ring. You can clearly see there must be a net force.

Even if you don’t work out that they all cancel in the case of the sphere, you can at least see that it is entirely unlike the ring in that at all locations within the sphere there are forces pointing in all directions which at least have a chance of canceling.

Now what if you make up a sphere from a series of rings? Take them as thin slices. Here each slice pushes (largely) in a direction perpendicular to the planes of the rings. However, now at any location in the sphere there are rings pushing (or pulling) both directions. Again, even if you don’t add it all up and see that it all cancels, you can clearly see that there are opposing forces with a chance to cancel.
 
  • #3
Thanks :) Need to do some thinking.
 
  • #4
Andrew Wright said:
Since you can construct shells from a series of rings, why would there be an electric field inside a single ring but not inside a shell?
When you construct a shell from a series of rings, you are carefully sizing and arranging the rings so that the non-zero fields of each individual ring cancel one another.

(and do remember that you can only construct a shell out of rings as an idealization, using an infinite number of rings all of zero height. Otherwise you won;t get a perfect spherical shell, but instead a sort of stepped thing lke a ball rendered on a computer screen with too few pixels. Calculating the electrical field inside such a object is going to be farly difficult, but it's easy to see that it won't be zero everywhere).
 
  • #5
So just to be clear there really is a field inside the ring but not inside the sphere?
Nugatory said:
When you construct a shell from a series of rings, you are carefully sizing and arranging the rings so that the non-zero fields of each individual ring cancel one another.

(and do remember that you can only construct a shell out of rings as an idealization, using an infinite number of rings all of zero height. Otherwise you won;t get a perfect spherical shell, but instead a sort of stepped thing lke a ball rendered on a computer screen with too few pixels. Calculating the electrical field inside such a object is going to be farly difficult, but it's easy to see that it won't be zero everywhere).
 
  • #6
Andrew Wright said:
So just to be clear there really is a field inside the ring but not inside the sphere?
Everywhere except at the exact center of the ring. (It’s worth taking a moment to figure out why - look for an image that illustrates “Newton’s shell theorem”, think about how it would work if applied to a ring).
 
Last edited:
  • #7
Thankyou!
 

1. How does the electric field inside a charged ring compare to that inside a charged spherical shell?

The electric field inside a charged ring is constant and uniform, while the electric field inside a charged spherical shell varies depending on the distance from the center. This is because the charge on a ring is distributed along its circumference, while the charge on a spherical shell is concentrated at its center.

2. What factors affect the strength of the electric field inside a charged ring or spherical shell?

The strength of the electric field inside a charged ring or spherical shell depends on the magnitude of the charge, the distance from the center, and the shape and size of the object. The electric field is stronger when the charge is larger and closer to the center, and weaker when the object is larger or more spread out.

3. How does the electric field inside a charged ring or spherical shell change as the distance from the center increases?

The electric field inside a charged ring decreases as the distance from the center increases, since the electric field is inversely proportional to the distance. On the other hand, the electric field inside a charged spherical shell initially increases as the distance from the center increases, but eventually becomes constant at a certain distance.

4. Can the electric field inside a charged ring or spherical shell be negative?

Yes, the electric field inside a charged ring or spherical shell can be negative. This occurs when the charge is negative and the electric field points towards the center. However, the magnitude of the electric field is always positive.

5. How does the electric field inside a charged ring or spherical shell affect charged particles placed inside?

The electric field inside a charged ring or spherical shell exerts a force on any charged particles placed inside. The direction of the force depends on the charge of the particle and the direction of the electric field. The magnitude of the force is also affected by the strength of the electric field at the location of the particle.

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