- #1
adenine7
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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 have a solid cylinder. It also now has charge density ρ. Find the electric field at the origin.
Homework Equations
Ering = kQz/(z2+ R2)3/2
σ =dq/2πRdz
Edisk = σ/2εo * (1 - z/(z2+R2)1/2)
ρ =dq/πR2dz
3. The Attempt at a Solution
I understand that to complete part a I must integrate the electric field of a charged ring (a distance z from its center) from z = 0 to z = ∞. I understand that to complete part b I must integrate the electric field of a charged disk (a distance z from its center) from z = 0 to z = ∞. Here is my solution to part a (I'm not sure if it's correct):
EHollow Cylinder = ∫0∞ kQz/(z2+ R2)3/2 dz = kσ2π/R
I don't know how to set up the integral for part b. When I integrate the equation for Edisk, with a dz tacked onto the end (not so sure about this), I get undefined. Is this a part of the problem, or is my math incorrect?