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Find the inductance of a unit length of ...

Find the inductance of a unit length of two parallel wires, each of radius a, whose centers are a distance d apart and carry equal currents in opposite direction. Neglect the flux within the wire.

A

`(mu_(0))/(2pi)In((d-a)/(a))`

B

`(mu_(0))/(pi)In((d-a)/(a))`

C

`(3mu_(0))/(pi)In((d-a)/(a))`

D

`(3mu_(0))/(3pi)In((d-a)/(a))`

Text Solution

Verified by Experts

The correct Answer is:
b
Sicne the wires are inifitem, so hthe sysrtem of tehwse two wires can be consideres as a closed ractangle of infinite length and breadth equat to d . Flux throught he strip of area l dr, due to current follwing in one wire is given by
`phi int_(a)^(d-a)(mu_(0)-I)/(2pir)(ldr)=(mu_(0)Il)/(2pi) ln ((d-a)/(a))`

The other wire produces the same result, so tha total flux through hte dotted rectangle is
`phi_("total")=(mu_(0)lI)/(pi)ln((d-a)/(a))`
The total inductance of length l,
`L=(phi_("total"))/(I)=(mu_(0)I)/(pi)ln((d-a)/(a))`
Inductance per unit length `(L)/(l)=(mu_(0))/(pi)ln((d-a)/(a))`
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