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?
Volume of a cylinder: pi*L*R^2
Gauss' Law: ∫ E·dA = E(pi*L*R^2) = Qinside*ε0
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 = (Qinside*pi*r^2)/ε0 = 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?