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What is the mutual inducatance of a syst...

What is the mutual inducatance of a system of coaxical cables carrying current in opposite directions a sshows in Fig. 4.3. Their radii are `a` and `b`, respectively.

Text Solution

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`B` between the space of the cables is `B = mu_(0)l//2 pi r`.
Ampere's law tells that `B` outside the cable is zero as the net current through the Amperian loop would be zero.

Taking an element of length `l` and thickness `dr`, flux through it is
`d phi = (mu_(0)l)/(2 pi r) ldr rArr phi = (mu_(0) Il)/(2 pi) int_(a)^(b) (1)/(r) dr = (mu_(0)lI)/(2 pi)` In `(b)/(a)`
`L = (phi)/(I) = (mu_(0)l)/(2 pi)` In `((b)/(a))`
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