Calculating Force Between 2 Conductors with Constant Currents

[Petar Mali]

Homework Statement

Is given two parallel conductors of equal and finite length [tex]L[/tex]. The distance between them is [tex]a[/tex]. On these conductors flow constant currents [tex]I_1[/tex], [tex]I_2[/tex] in same dirrections. If the line which connecting their centars built angle [tex]\alpha[/tex] whith dirrection of conductor find the force that the first conductor interract to second.

Homework Equations

The Attempt at a Solution

In solution is force given by

[tex]\vec{F}_{21}=I_2\int^{\frac{L}{2}+actg\alpha}_{-\frac{L}{2}+actg\alpha}dz\vec{e}_z\times \vec{B}_1[/tex]

Why the boundaries are [tex]-\frac{L}{2}+actg\alpha[/tex] and [tex]\frac{L}{2}+actg\alpha[/tex]?

Tnx for your answer!

Homework Statement

Homework Equations

The Attempt at a Solution

 

[NateD]

The two conductors are parallel, so the magnetic field from each conductor will be in the same direction. The line that connects the centers of the two conductors forms an angle $\alpha$ with the direction of the conductor. Thus, the force between the two conductors is given by: \vec{F}_{21}=I_2\int^{\frac{L}{2}+actg\alpha}_{-\frac{L}{2}+actg\alpha}dz\vec{e}_z\times \vec{B}_1The boundaries are set in this way because they represent the points on the line connecting the centers of the two conductors which have the same angle $\alpha$ with the direction of the conductor.