- #1
Liquidxlax
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Homework Statement
Show that a conductive shell a<b has a resistance of
R= (a-1-b-1)/(4πσ)
Homework Equations
J = σE I = JA = σEA
R=(Va-Vb)/I
The Attempt at a Solution
My problem is my algebra i think.
First i found the electric field
Qenc= ρV = (Qr3)/(b3-a3)
E= (4πkQenc)(4πr2) = (KQr)/(b3-a3)
solve for potential
(Va-Vb)= (kQ)/(2(a-b))
Next step is where i think i messed up
I=σEA = [(KQr)/(b3-a3)]σ(4πr2)
= (4πKQσr3)/(b3-a3)
I insert for r3 for (b3-a3)
and get 4πKQσ=I
then R= V/I
[(kq)/(2(a-b))]/(4πKQσ) = (a-1-b-1)/(8πσ)
which isn't right. thanks for the help, hope its not to messy