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## Homework Statement

Consider the cross sections of two, very long, concentric, metallic, hollow cylinders placed in a vacuum. The small cylinder has inner radius A and outer radius B while the larger cylinder has inner radius

**2A**and outer radius

**2B**. Initially the small and big hollow cylinders have charge densities of

**+2λ and -2λ**respectively.

1) AT

**electrostatic equilibrium**what is the total charge of the inner surface of the big cylinder if the cylinders both hav e length

**L**?

2) what is the

**electric field**in tha cavity between the two cylinders? se r as the distance measured from the center of the spheres.

## Homework Equations

relevant equations would be the flux which is EA=Q

_{enc}/ε

_{o}

## The Attempt at a Solution

for number 1

since this is at electrostatic equilibrium, the net charge AT the CYLINDER is ZERO. therefore Q

_{in}=0... but inner cylinder has +2λL, and so the inner surface of the larger cylinder would be -2λL... and for the outside surface.... (will it be +2λL for the net charge on the conductor to be zero.?? or there will be

**no charge**because the said "net" charge in that conductor should be -2λL??) i'm confused....

and is it correct for me to multiply the charge densities to L??

for number 2

I set up an equation like this...

EA= E2πrL = ([2λ(πr

^{2}L)] - [-2λ(πR

^{2}L)]) /ε

_{o}

we cancel and it becomes like this

E = [λπ(r

^{2}+R

^{2})] /ε

_{o}r

where r is the outer radius of the smaller cylinder and R is inner radius of larger one.. i think i'm wasting my effort because all this is wrong :-ss please help.

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