Which electric field is larger?

[-EquinoX-]

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 distance x away from the center of the ring. Now the charge Q is spread uniformly over the circular area the ring encloses, forming a flat disk of charge with the same radius. How does the field Edisk produced by the disk at P compare to the field produced buy the ring at the same point? (a) Edisk < Ering (b) Edisk = Ering (c) Edisk > Ering (d) impossible

Homework Equations

The Attempt at a Solution

I'd say the answer is Ering > Edisk based on my logical perception ... can anyone tell me if this is true?

 

[rl.bhat]

In the ring all the charges at the same distance from the point i.e. d = sqrt( x^2 + R^2).
When you spread on the disc of same radius R, all the charges are not at the same distances. If you divide the ring into circular strips of equal thickness, inner rings are closer to the point then the outer rings. Electric field is inversely proportional to the square of the distance. Hence field due to the disc is more than the ring.

 

[chrisk]

Open the link below for a good analysis of axial electric fields from a ring of charge and and disk with uniform charge density. This should help.

http://www.ux1.eiu.edu/~cfadd/1360/23EFields/Continu.html