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Question

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

A
μ02πln(daa)
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B
μ0πln(daa)
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C
3μ0πln(daa)
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D
μ03πln(daa)
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Solution

The correct option is B μ0πln(daa)
Since, the wires are infinite, so the system of these two wires can be considered as closed rectangle of infinite length and breadth equal to d.
Flux through strip
ϕ=daaμ0I2πr(Idr)=μ0Π2πln(daa)
The other wire produces the same result, so the total flux through the rectangle ABCD is
ϕtotal=μ0Ππln(daa)
The total inductance of length l
L=ltotalI=μ0Iπln(daa)
Inductance per unit length =LI=μ0πln(daa)
728034_669990_ans_3746bed569bf49da8cd6b81c1a614771.png

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