Question

Continuous charge distribution

Answer 1

Q=Sigma*2pi*R*w
dQ=Sigma*dA
Integrate both sides
Q=Sigma*2pi((R^2-(R^2-2RW+W^2))
Is this correct

Answer 2

Q=Sigma*2pi*R*w is correct

Since w << R, no need to integrate.

Answer 3

but the correct answer is Q/4pi*R*w

Answer 4

For a single side wont it be Q/4pi*R*W and for the two sides Q/2pi*R*w

Answer 5

I see, since both sides will be equally charged, there will be a Q/4pi*R*W front AND back charge density