Electric Field Due To A Ring and Disk

[Bashyboy]

Homework Statement

Assume a uniformly charged ring of radius R and charge Q produces an electric field E_ring at a point P on its axis, at a distance x away from the center of the ring. Now the same charge Q is spread uniformly over a circular area the ring encloses, forming a flat disk of charge with the same radius. How does the E_disk produced by the disk at P compar with the field produced by the ring at the same point?

(a) E_disk < E_ring

(b) E_disk = E_ring

(c) E_disk > E_ring

(d) Impossible to determine

Homework Equations

The Attempt at a Solution

My first suspicion was, that E_disk > E<sub>ring was the correct answer. This was so, because the disk can be thought of as many rings of infinitesmal size concentric. One infinitesmal ring would contribute to the electric field that is directed co-axially. This co-axial would begin to compound as you considered the remaining infinitesmal rings that constitute the entire disk.

Here is where came to a hault:

As you consider infinitesmal rings further from the center of disk, the angle that the infinitesmal ring makes with the x-axis becomes greater, thereby causing the co-axial component fo the electric field to dimish, as you move from the center of the disk.

In addition, I have this conjecture that the answer would also somehow depend on the relative of magnitude of x and R.

Could someone help me?</sub>

 

[greendog77]

Consider the vectors of the electric field that each small portion of the disk generates, and compare it to the vectors that each small portion of the ring generates.

 

[haruspex]

As you consider infinitesmal rings further from the center of disk, the angle that the infinitesmal ring makes with the x-axis becomes greater, thereby causing the co-axial component fo the electric field to dimish, as you move from the center of the disk.

I'm puzzled as to why you're puzzled. The charge on the ring is on average further from the centre than for the disk, giving the answer you have.

 

[Bashyboy]

My first suspicion was, that E_disk > E_{ring was the correct answer. This was so, because the disk can be thought of as many rings of infinitesmal size concentric. One infinitesmal ring would contribute to the electric field that is directed co-axially. This co-axial would begin to compound as you considered the remaining infinitesmal rings that constitute the entire disk.}

Well, I wasn't sure if this idea conflicted with is one:

As you consider infinitesmal rings further from the center of disk, the angle that the infinitesmal ring makes with the x-axis becomes greater, thereby causing the co-axial component fo the electric field to dimish, as you move from the center of the disk.

In addition, I have this conjecture that the answer would also somehow depend on the relative of magnitude of x and R.

 

[haruspex]

Well, I wasn't sure if this idea conflicted with is one:

Seems to me they agree.