A solid, infinite metal cylinder of radius a = 1.5 cm is centered on the origin,

Question

A solid, infinite metal cylinder of radius a = 1.5 cm is centered on the origin, and has charge density inner = -5 nC/cm. Surrounding this cylinder is a cylindrical metal shell of inner radius b = 3.0 cm and outer radius c = 4.5 cm. This shell is also centered on the origin, and has total charge density shell = +2 nC/cm.

Find the potential difference Va - Vc between the surface of the metal cylinder (r = a) and the outer surface of the metal shell (r = c).

Where I'm stuck:

I'm completely baffled on how to approach this type of problem. First I tried to calculate  Va and Vc separately using the formula for finding V due to a continuous line of charge.

However, since the cylinders are infinite, this doesn't work and I haven't been able to find a way to cancel out the infinity terms.

I'm not sure how to go about solving this. Any suggestions?

Explanation / Answer

Letting y = charge/length and e the permittivity constant Flux = E * A = q / e Gauss Law E * 2 * pi * R * L = y L / e E = y / (2 * pi * e * R) E = - dV / dR V = [y / (2 * pi * e)] ln (R2 / R1) I included -y in the integration (Going from a lower to higher potential)

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