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(d−aa)
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B
μ0πln(d−aa)
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C
3μ0πln(d−aa)
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D
μ03πln(d−aa)
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Solution
The correct option is Bμ0πln(d−aa) 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=∫d−aaμ0I2πr(Idr)=μ0Π2πln(d−aa) The other wire produces the same result, so the total flux through the rectangle ABCD is ϕtotal=μ0Ππln(d−aa) The total inductance of length l L=ltotalI=μ0Iπln(d−aa) Inductance per unit length =LI=μ0πln(d−aa)