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What is the mutual inductance of a syste...

What is the mutual inductance of a system of co-axial cables carrying current in opposite directions as shown ? Their radii are a and b respectively and its length `l`.

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The B between the space of the cables is B `=mu_(0)I/2 pir ` The Ampere.s law tells that B outside the cables is zero as the net current through the amperian loop would be zero . Taking an element of length `l` and thickness dr `d phi` through it is
`dphi=(mu_(0)I)/(2pir)ldrimplies phi =(mu_(0)Il)/(2pi)int_(a)^(b)(1)/(r)dr = (mu_(0)lI)/(2pi)."In" (b)/(a)`
`L=(Phi)/(I)=(mu_(0)l)/(2pi)"In"((b)/(a))`
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