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Solved Problems-14

Problem-14
Determine the self-inductance of a coaxial cable of inner radius ‘a’ and outer radius ‘b’ when the inner conductor is solid.
Solution
Here, we have to find two inductances:
(1) Internal inductance, Lin, considering the flux linkages due to the inner conductor
(2) External inductance, Lext, considering the flux linkages between the inner conductor and the outer conductors

Coaxial cable
 
Now, magnetic energy stored in the inductor is,
Description: Description: 104656.png
where Description: Description: 104646.png

(a) For 0 ≤ r ≤ a:
By Ampere’s law,
Description: Description: 104632.png
Description: Description: 104625.png
 
Description: Description: 104618.png
 
(b) For a ≤ r ≤ b:
By Ampere’s law,
Description: Description: 104610.png
 
Description: Description: 104591.png
 
Hence, the total inductance of the coaxial cable is,
Description: Description: 104580.png



 





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