# Force Between Cylindrical Capacitor Plates

1. Sep 15, 2008

### maxmax1

1. The problem statement, all variables and given/known data

Capacitor plates are length L with radii a,b a<b are co-axial and intially covering eachother with line charge density of the inner plate Q/L.

determine the force between plates as the inner plate is partially withdrawn along the axis.

i) if cylinders charged to voltage V and then discnnected
ii) if cylinders remain connected and maintained at voltage V

2. Relevant equations

u=(1/2)cv^2=(1/2)qv F=-du/dL

voltage between plates = Qln(b/a)/2Lpi*e0

capacitance between plates = 2Lpi*e0/ln(b/a)

3. The attempt at a solution

using partial derivitives. for

i) hold q constant differentiate for V

du=(1/2)qdv

-du/dl=(-1/2)Q(d/dL)(Qln(b/a)/2Lpi*e0)

= (1/4)(Q^2)ln(b/a)/2(L^2)pi*e0)

and is directed same direction to one being removed..

using partial derivitives. for

i) hold v constant differentiate for q

du=(1/2)(v^2)dc

-du/dl=(-1/2)(v^2)(d/dL)(2Lpi*e0/ln(b/a))

= (-1/2)(v^2)(2pi*e0/ln(b/a))

and is directed in opposite direction to one being removed

Are this working OK?

Many thanks!