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## Homework Statement

Two very long hollow conducting cylindrical shells are situated along the x-axis. The shells are concentric and have negligible thickness. The inner shell has a radius a and a linear charge density +lambda, while the outer shell has a radius b and a linear charge density -lambda. Take the zero of electrostatic potential to be at r = 0. The coordinate r measures the distance from the common axis of the two cylinders in a region far from either end.

a) Determine the electrostatic potential V(r) for all values of r

b) Sketch V(r) vs. r for all r

c) Determine the potential difference DeltaV between r=a and r=b

d) If a positive charge +q is released from rest at r=a, what will be its kinetic energy when it reaches the outer cylinder at r=b.

## Homework Equations

V(r)=q/4piE0r

Delta V=Vb-Va=q/4PiE0*(1/rb-1/ra)

Ke=1/2mv^2

U=kq1q2/r

KEf=Ui

## The Attempt at a Solution

a) at r=a

V=q/4piE0a

at r=b

V=q/4piE0b

b) as the radius increases the potential goes down. It starts at some positive y value and ends at some negative y value.

c)Delta V=Vb-Va=q/4PiE0*(1/b-1/a)

d) U=kq1q2/a

1/2mv^2=kq1q2/r

v^2=2kq1q2/mr

v=(2kq1q2/mr)^1/2