# Insulating Cylindrical Shell, Potential at edge

1. Jul 8, 2012

### wohzah

1. The problem statement, all variables and given/known data

A long cylindrical insulating shell has an inner radius of a = 1.37 m and an outer radius of b = 1.60 m. The shell has a constant charge density of 2.70 10−9 C/m3. The picture shows an end-on cross-section of the cylindrical shell.

What is the magnitude of the electric field at a distance of r= 1.81 m from the axis?
5.76×101 N/C

What is the magnitude of the electric field at a distance of r= 1.52 m from the axis?
4.35×101 N/C

If we take the potential at the axis to be zero, what is the electric potential at the outer radius of the shell?

2. Relevant equations
V=kdq/r

Va - Vb=∫E.da

3. The attempt at a solution
∫ Q*(R^2 - r^2) / 2r *ε0 from the inner radius to the outer radius, my assumption was that since V equals the summation of electric field over the area enclosed, and that since potential was zero at the center, the potential would be equal to the difference in potential due to the electric field. Any insight or help is appreciated.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 8, 2012

### wohzah

hey for those interested I actually sorted myself out on this one, the final equation i used was the integral of rho(r^2 -a^2)*dr / 2 *r* e0 [a,R]. Where rho is the charge density, a is the interior radius, r is a variable, dr is the differential radius element, and e0 is epsilon naught, 8.854e-12.