Calculating free charge from a LIH material

[Prometheus]

I need to find the free charge per unit length, λ, on a cylinder which is surrounded by a LIH dielectric material (which itself is encased by another tube).

 

I've already found the electrostatic potential V® from which i've found E.

 

From this i can find D easily as D= εε₀E.

 

Then i use this integral version of Gauss's law: [math]\int_S[/math] D.dS=Q_f.

Using the cylindrical symmetry of the situation i get: D_r2πrL = Q_f

Then i just plug in my values and get an answer.

 

 

 

The question is what am i missing? The question is worth a barrel of marks and the above seems too simple. I've deliberately omitted details as i just want a nudge in the right direction, but can supply them if needed.

 

As always, all help greatly appreciated.

[Sensei]

You have cylinder (fill inside) or tube (hole inside)?

If electrons will gather just on surface area, they should be spread quite evenly.

Area of cylinder is area of top + area of bottom + area of sides: A=pi*r^2+pi*r^2+2pi*r*h

 

Tube (hole inside) has much bigger area. With meaningless thickness, it has front side and back side.

Edited January 31, 2016 by Sensei

[Prometheus]

A metal cylinder surrounded by a tube of LIH material surrounded by another metal tube. I need to find the free charge per unit length on the inner cylinder. It's described as long, which so far in the course has always been an invitation to assume it's infinitely long.