How Do You Apply Gauss's Law to a Non-Uniformly Charged Non-Conducting Cylinder?

[lcam2]

1. Homework Statement
A long, solid, non-conducting cylinder of radius 8 cm has a non-uniform volume density, ρ, that is a function of the radial distance r from the axis of the cylinder. ρ = A*r2 where A is a constant of value 3 μC/m5.

Homework Equations

Gauss's law EA = Q/(epsilon)
Q(enclosed)= Pv
Volume of cylinder = 2*(PI)*r*L

The Attempt at a Solution

Part a can be done using gauss's law, and integrating Q(enclosed)= pv; since the volume density is not constant.
The problem is part b, where the point where I have to calculate the field is outside the Gaussian surface.

 

[Doc Al]

The problem is part b, where the point where I have to calculate the field is outside the Gaussian surface.

That's a puzzling statement, since you put the Gaussian surface wherever you need to in order to find the field. Please state the complete part b question.

 

[lcam2]

Im sorry i didn't notice it was missing,

(a) What is the magnitude of the electric field 6 cm from the axis of the cylinder?

(b) What is the magnitude of the electric field 10 cm from the axis of the cylinder?

 

[Doc Al]

(b) What is the magnitude of the electric field 10 cm from the axis of the cylinder?

OK, so what's the problem in applying Gauss's law to solve this part, just like part a?

Hint: Your Gaussian surface will have a radius of 10 cm.

 

[lcam2]

so, basically what you are saying is that the original radius of the cylinder does not matter, am I correct?

 

[Doc Al]

so, basically what you are saying is that the original radius of the cylinder does not matter, am I correct?

It matters in that it tells you the extent of the charge distribution. But it doesn't prevent you from having a Gaussian surface outside of the cylinder.

 

[lcam2]

Ok, thank u!