- #1

Liquidxlax

- 322

- 0

## 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=(V

_{a}-V

_{b})/I

## The Attempt at a Solution

My problem is my algebra i think.

**First i found the electric field**

Q

_{enc}= ρV = (Qr

^{3})/(b

^{3}-a

^{3})

E= (4πkQ

_{enc})(4πr

^{2}) = (KQr)/(b

^{3}-a

^{3})

**solve for potential**

(V

_{a}-V

_{b})= (kQ)/(2(a-b))

**Next step is where i think i messed up**

I=σEA = [(KQr)/(b

^{3}-a

^{3})]σ(4πr

^{2})

= (4πKQσr

^{3})/(b

^{3}-a

^{3})

I insert for r

^{3}for (b

^{3}-a

^{3})

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