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Hi all. Trying to find electric field of a disk with a charge density of D and a radius R (let us assume it has a thickness h). I know you can do so by breaking up the disk into concentric rings and integrating coulombs law. However, i would like to go about using gauss's law if that is possible. So:

Let k = permittivity of free space (usual symbol: epsilon)

(integral of) (E*dA) = Q_{Enc}/k

gonna use a cylinder as a gaussian surface (pillbox).

E * (integral of) (dA) = Q_{Enc}/k

Q_{Enc}= D*V(integral of) (dA) = (2*pi*R^2) + (2*pi*R*h) = 2*pi*R * (R + h)

=> E * 2*pi*R*(R+h) = (D*V)/k

=> E = (D*V) / (k*2*pi*R*(R+h))

V = h*pi*R^2

=> E = (D*h*pi*R^2) / (k*2*pi*R*(R+h))

=> E = (D*R*h) / (2*k*(R+h))

this is my final answer, i know it's probably wrong but i have no idea why. Also using coulombs law as mentioned above does not leave an h variable (thickness of the cylinder) in the final equation. Can someone please shed some light as to what my problem is?

P.S: My final goal is to find the electric potential of a point on the disk's axis a distance x from the middle of the disk. My book uses V = (integral of) dQ/r but i'm trying to use V_{a}- V_{b}= (integral of E*dL), So that is why i'm trying to find the E-field. Help provided for calculating electric Potential of disk will be greatly appreciated.

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# Electricfield of a Disk using Gauss's law

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