Capacitance per length unit of coaxial cable

[gruba]

Homework Statement

Coaxial cable has double layered dielectric.
a=2mm, b=4mm, c=8mm, ε_r1=3, ε_r2=4.5, U_ab=1000V
1. Calculate capacitance per unit length of a cable.
2. Calculate inner and outer charge densities of a cable.
2. Homework Equations
Gauss law
C^'=Q^'/U
σ = nD
σ_p = nP
3. The Attempt at a Solution
After applying Gauss law for dielectrics, I get electric field:
E=Q^'/(2πε₀(ε_r1+ε_r2r)).
Limits of integration for voltage: (a - b) + (b - c)
U=(Q^'(ln(b/a)+ln(c/b)))/(2πε₀(ε_r1+ε_r2))

Then, C^'=(2πε₀(ε_r1+ε_r2))/(ln(b/a)+ln(c/b))
This gives me C^'=288pF/m but in my books solution it is C^'=144pF/m.

Could someone check this.
Thanks for replies.

 

[mfb]

E shouldn't have the same formula in both parts, it has to include the local ε somehow. Also, in the way you wrote it the units do not match.
I'm surprised that your answer seems to be exactly a factor of 2 off with this, however.