Fields inside charged rings vs spherical shells

[Andrew Wright]

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?

 

[Cutter Ketch]

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.

 

[Andrew Wright]

Thanks :) Need to do some thinking.

 

[Nugatory]

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).

 

[Andrew Wright]

So just to be clear there really is a field inside the ring but not inside the sphere?

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).

 

[Nugatory]

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).

 

[Andrew Wright]

Thankyou!