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.

Step-by-step solution

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 = _a^ d-a ₀ I 2 r (l d r)= ₀ I 2 ( d-a a ) The other wire produces the same result, so the total flux through the rectangle A B C D is _ total = ₀ I I ( d-a a ) The total inductance of length 1 L= I_ total I = ₀ I ( d-a a ) Inductance per unit length = L l = ₀ ( d-a a )