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## 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 2.9 μC/m5.

What is the magnitude of the electric field 7 cm from the axis of the cylinder?

## Homework Equations

Volume of a cylinder: pi*L*R^2

Gauss' Law: ∫ E·dA = E(pi*L*R^2) = Q

_{inside}*ε

_{0}

## The Attempt at a Solution

ρ = A*r2 = (2.9x10^-6)*0.7^3 = 1.421e-8

ρV = (1.421x10^-8)* pi*0.7^2 = 2.18745955e-10

E = (Q

_{inside}*pi*r^2)/ε

_{0}= 5.433109096 N/C

That does not look right at all to me, and I am not sure where my set up went wrong. Its obvious to me that I did not need the length of the cylinder so I ommited L (actually assumed a value of 1). Did I get the volume correct?