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:F/L = μ0*I²/2πd

Explanation:

Both wires carries current of the value (I) and are separated by the distance (d).

The length of both wires is (L).

The first wire creates a magnetic field of the magnitude according to Bio-savart law

B = (Uo * I) / 2πd

This magnetic field has the ability to exert a force F on the second wire.

This force (F) is given as

F=BIL * sin θ

θ here is 90 because the magnetic field is perpendicular to the length of the second wire.

Thus the value of sin 90 = 1

Hence F = BIL

But B = (Uo * I) / 2πd.

We have that F = B=[ (Uo * I) / 2πd] x IL

Thus we have that F = [Uo * I²/2πd] x L

By rearranging, and bringing L to the left hand side of the equation, we have that

F/L = [Uo * I²/2πd]