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user3
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A coaxial cable is modeled as a long thin cylindrical shell with radius b concentric with a solid wire of radius a (the wire is inside the shell). Calculate the inductance of a length l of this cable.
(Example 32.5 Here) ---> https://echsphysics.wikispaces.com/file/view/APPhysicsCH32.pdf
the solution in my textbook is as follows: take a thin rectangular slice between the inner wire and the outer shell. If we assume that the outer shell and the inner wire are connected at the two ends of the cable, that rectangular slice can be imagined as a very long loop (with length l) in an solenoid. We get the flux through this long rectangular slice, then the inductance is just L=ϕ/I
My question is: By definition, the inductance of a solenoid is L=Nϕ/I where is the number of loops. Now if we considered the rectangular slice to be a loop among many that form the coaxial cable, shouldn't the inductance be L=(2∏b)ϕ/I or something? shouldn't there be term equivalent to the N in the solenoid inductance equation because the magnetic field is passing through many of these long rectangular slices?
(Example 32.5 Here) ---> https://echsphysics.wikispaces.com/file/view/APPhysicsCH32.pdf
the solution in my textbook is as follows: take a thin rectangular slice between the inner wire and the outer shell. If we assume that the outer shell and the inner wire are connected at the two ends of the cable, that rectangular slice can be imagined as a very long loop (with length l) in an solenoid. We get the flux through this long rectangular slice, then the inductance is just L=ϕ/I
My question is: By definition, the inductance of a solenoid is L=Nϕ/I where is the number of loops. Now if we considered the rectangular slice to be a loop among many that form the coaxial cable, shouldn't the inductance be L=(2∏b)ϕ/I or something? shouldn't there be term equivalent to the N in the solenoid inductance equation because the magnetic field is passing through many of these long rectangular slices?