Calculating charge on capacitor.

[Miike012]

The problem and solution are in the document.

My question is in regards to the solution about calculating the charge on the capacitor. Would an equally correct solution for the charge be...
Let σ_s be the surface charge density on the plate.
The plate is a conductor and I would assume that the thickness throughout the plate is uniform, and there should be no divots or anything that would create the charge density in some area of the plate to be greater than another area of the plate.

Thus σ_s is uniform.

Therefore Q = ∫_sσ_sds = σ_s[∫_sds] =
σ_s[(pi)(a²)] where a is the radius of the circular capacitor.
(ds is obviously a differential surface area of the capacitor)

FINAL: Charge of capacitor (Q) = σ_s[(pi)(a²)]

 

[Simon Bridge]

Yes - if you know the surface charge density.

In the attachment problem, you don't know the surface charge density.

For a finite conducting plate, the surface charge density will not, generally, be uniform: like charges repel so there may be a higher charge density towards the outer edges of the plate. In the attachment problem, the dielectric has a radially dependent constant - so the charge distribution is certainly not uniform (as E is not uniform).