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.
relevant equations would be the flux which is EA=Qenc/εo
The Attempt at a Solution
for number 1
since this is at electrostatic equilibrium, the net charge AT the CYLINDER is ZERO. therefore Qin=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(πr2L)] - [-2λ(πR2L)]) /εo
we cancel and it becomes like this
E = [λπ(r2+R2)] /εor
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.