I'm not sure I understand the question. The capacitor is 3 concentric cylinders, and the only wire in the problem is connecting the inner and outer cylinders (I guess this means they are connected in series?).
Thanks for the reply!
Ok, so treating it as two capacitors (Where V1 is potential difference for the inner two cylinders and V3 is potential difference for the outer two cylinders):
V1 = -∫R2R Q / 8πεLR dR = -Qln(2) / 8πεL = Qln(1/2) / 8πεL
C= Q / V, so C1 = 8πεL / ln(1/2)
Same thing for C3...
Homework Statement
I'm trying to find the capacitance of a system of 3 concentric hollow cylinders. The first cylinder has radius R, the second radius 2R, the third radius 3R. Cylinders 1 and 3 are connected by a wire. In total, they have charge +λ, and the second cylinder has charge -λ. The...
Expressing my electric field for a hollow cylinder in terms of εo, I get σ / 2εo. So, this is the same as the electric field for an infinite sheet of charge at distance z away?
For part b., I changed the expression for σ (fixed the area of a disk) and got σ = ρdz. I did what you said and...
Part a.
If I integrate kσ2πRz/(z2+ R2)3/2 dz from 0 to ∞ I get kσ2π, which checks out with dimensions. I believe I was forgetting to integrate with the extra z in the numerator (which does not get replaced by dz).
Part b.
Thank you for explaining the difference between ρ and σ! I thought they...
Thanks for the reply!
I think I made a mistake typing that in; the equation I integrated (which I did not correctly transcribe, sorry for the confusion) is with dQ = σ2πRdz (that's why my final answer has σ2π in it).
Assuming this is the correct answer, here's where I get stuck with part b...
Homework Statement
Part a.
A cylinder (with no face) is centered symmetrically around the z axis, going from the origin to infinity. It has charge density σ and radius R. Find the electric field at the origin.
Part b.
Same problem, except this time instead of a hollow cylinder with no face we...