# Electric field between two concentric cylinders

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This is a question that has been bothering for a while. I don't know if my answer is correct or not, but anyone look over it?

Both cylinders have the same length L. The first cylinder with radius R1 has a charge Q1 uniformly distributed inside the cylinder. The second cylinder is a conductor with radius R2 and charge Q2 (negative) uniformly distributed into the area between the first and second cylinder.

Find the electric field when:

a) r < R1 ; b) R1< r< R2;  c) r> R2

So, I did it like this.

a) r< R1

$∮ E.dA = E2πrL = Qi/ε₀$

$Qi= ρV= [Q1/(πLR1^2)]*πLr^2$

$E= rQ1/(2πLε₀R1^2)$

b) R1< r < R2

$∮ E.dA = E2πrL = Qi/ε₀$

$E= Q1/ (2πrLε₀)$

c) r> R2

$E1= Q1/ (2πrLε₀) and E2= -Q2/ (2πrLε₀)$ (because Q2 is negative I put the minus in front of it)

$Eout = E1 + E2 = Q1/ (2πrLε₀) -Q2/ (2πrLε₀)$

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