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gruba
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Homework Statement
Two cylindrical conductors, of distance between them d and radius a (a<<d), have dielectric layer of relative permitivitty εr and thickness a. Calculate capacitance per unit length of this system.
Homework Equations
Capacitance per unit length, C'=Q'/U
Gauss law, cylindrical symmetry, E=Q'/(2πεr2)
The Attempt at a Solution
I have started with the equation C'=Q'/U.
Voltage integration limits: (a - 2a) + (2a - (d-2a)) + ((d-2a) - (d-a))
After calculating the partial integrals, voltage U is:
U=Q'(ln2/εr+ln((d-2a)/(2a))+ln((d-a)/(d-2a))/εr)
Applying voltage in the expression for capacitance per unit length gives
C'=2πε0/(ln2/εr+ln((d-2a)/(2a))+ln((d-a)/(d-2a))/εr)
In my books solution, in the numerator there is πε0 for C'.
Are my limits of integration for voltage correct? Maybe it is a mistake in books solution.
Thanks for replies.