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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^{'}/(2πε_{0}(ε_{r1}+ε_{r2}r)).
Limits of integration for voltage: (a  b) + (b  c)
U=(Q^{'}(ln(b/a)+ln(c/b)))/(2πε_{0}(ε_{r1}+ε_{r2}))
Then, C^{'}=(2πε_{0}(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.
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