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Capacitance per length unit of coaxial cable

  • #1
208
1

Homework Statement


Coaxial cable has double layered dielectric.
a=2mm, b=4mm, c=8mm, εr1=3, εr2=4.5, Uab=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
σp = nP

3. The Attempt at a Solution

After applying Gauss law for dielectrics, I get electric field:
E=Q'/(2πε0r1r2r)).
Limits of integration for voltage: (a - b) + (b - c)
U=(Q'(ln(b/a)+ln(c/b)))/(2πε0r1r2))


Then, C'=(2πε0r1r2))/(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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Answers and Replies

  • #2
33,927
9,662
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.
 

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