Question

Two identical long wires of radius a = 2.80 mm are parallel and carry identical currents of i = 5.00 A in opposite directions. Their center-to-center separation is W = 19.0 cm. Neglect the flux within the wires but consider the flux in the region between the wires. What is the inductance per unit length of the wires?

Answer 1

Answer:

Inductance per unit length, $\frac{L}{l} = 7.02 * 10^{-7} H/m$

Explanation:

Radius of the wire, a = 2.80 mm

Currents carried by each of the wires, i = 5.00 A

Center-to-Center Separation, W = 19.0 cm

The flux in the wires is given by the equation, ∅ = Li

The Net flux of the region between the wires  is given by the equation:

$\phi = \frac{l \mu_0 i}{\pi} ln(\frac{W-a}{a})$

Divide both sides by l to get the net flux per unit length

$\phi/l = \frac{ \mu_0 i}{\pi} ln(\frac{W-a}{a})\\\phi/l = \frac{ 4 \pi * 10^{-7} i}{\pi} ln(\frac{0.019-0.0028}{0.0028})\\\phi/l = 7.02 * 10^{-7} i\\\frac{Li}{l} = 7.02 * 10^{-7} i\\\frac{L}{l} = 7.02 * 10^{-7} H/m$