- #1

Aero6

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## Homework Statement

A long coaxial cable carries a volume charge density rho=alpha*s on the inner cylinder (radius a) and a uniform surface charge density on the outer cylindrical shell (radius b). This surface charge is negative and of just the right magnitude so that the cable as a whole is electrically neutral.

a)Find the electric field in each of the three regions:

s<a, a<s<b, s>b

b)find the potential difference in each of these regions with a refernce point at infinity

## Homework Equations

Gauss's law integral of E*da = Qencl/epsilon

V=-integral E*dl

## The Attempt at a Solution

b) a<s<b

I'm confused about integrating to find Qencl. Qencl=integral rho*dtao where dtao=s*ds*dtheta*dz, but when I set up the bounds on the integral for s, I don't understand which bounds I am supposed to include. Since there is a less than sign and not a less than or equal to sign when the problem says that s is greater than a and less than b, how is it okay to integrate so from a to an arbitrary distance that is less than b? Isn't this still including the distance a, which we shouldn't do because of the strict greater than sign? Also, how would this problem change if I was asked to find the electric field in the region: s is greater than OR equal to a and less than or equal to b?

Thank you