Question

You are given two infinite, parallel wires each carrying current I. The wires are separated by a distance d, and the current in the two wires is flowing in the same direction. This problem concerns the force per unit length between the wires.
What is the force per unit length F/L between the two wires?
Express your answer in terms of I, d, and constants such as μ0 and π.

Answer 1

Answer:

$\dfrac{F}{L}=\dfrac{\mu_oI^2}{2\pi d}$

Explanation:

If the current flowing in two wires is I and they are separated by a distance of d. We know that the magnetic field due to a wire is given by :

$B=\dfrac{\mu_oI}{2\pi d}$

Where

d is the separation between wires

The magnetic force between the wires is given by :

$F=BIL$

I is the current in wire

L is the length of the wires

$F=\dfrac{\mu_oI^2L}{2\pi d}$

The magnetic force per unit length is given by :

$\dfrac{F}{L}=\dfrac{\mu_oI^2}{2\pi d}$

So, the force per unit length F/L between the two wires is $\dfrac{\mu_oI^2}{2\pi d}$. Hence, this is the required solution.