• Support PF! Buy your school textbooks, materials and every day products Here!

Electric Field Due To A Ring and Disk

  • Thread starter Bashyboy
  • Start date
  • #1
1,421
5

Homework Statement


Assume a uniformly charged ring of radius R and charge Q produces an electric field Ering 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 Edisk produced by the disk at P compar with the field produced by the ring at the same point?

(a) Edisk < Ering

(b) Edisk = Ering

(c) Edisk > Ering

(d) Impossible to determine

Homework Equations





The Attempt at a Solution



My first suspicion was, that Edisk > Ering 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?
 

Attachments

Answers and Replies

  • #2
25
0
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.
 
  • #3
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,465
5,411
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.
 
  • #4
1,421
5
My first suspicion was, that Edisk > Ering 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.
 
  • #5
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
33,465
5,411
Well, I wasn't sure if this idea conflicted with is one:
Seems to me they agree.
 
  • Like
Likes 1 person

Related Threads on Electric Field Due To A Ring and Disk

  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
1
Views
15K
  • Last Post
Replies
2
Views
12K
Replies
4
Views
1K
Replies
1
Views
6K
Replies
3
Views
16K
Replies
3
Views
1K
  • Last Post
Replies
2
Views
526
Replies
6
Views
4K
Replies
4
Views
5K
Top