Net magnetic force on circuit segment due to 2 parallel wires

[risakapal]

Homework Statement

Two long, parallel wires are separated by a distance d and carry current I flowing in opposite directions, as shown in the figure. A circuit segment of length L is parallel to the long wires and carries a current of I' flowing in the direction shown. The circuit segment is at distance R from the wires. The +z direction is to the right, the +x direction is up, and the +y direction is out of the screen. Approximate the net magnetic force F acting on the circuit segment in terms of the given quantities and physical constants, assuming that R >> d. Express the force using ijk unit vector notation.

Relevant Equations

F∝ l x B
Do not approximate the distance between each wire and the wire segment as 𝑅. Rather, make approximations when comparing higher orders of 𝑅 and 𝑑. For example, assume that 𝑅^2 + 𝑑^2 ≈ 𝑅^2, and so forth.

This answer is incorrect when I try submitting it.

 

[BvU]

Hi,
A bit hard to read on my phone, but: what is the ijk notation () and which way is the force ?

 

[risakapal]

Hi,
A bit hard to read on my phone, but: what is the ijk notation () and which way is the force ?

Thank you for your response. Would the force on the circuit be to the left since the wire with the current in the same direction is closer? I thought it might be in the negative z-direction.

 

[BvU]

Hmm, i am lost a bit -- think you're right...

 

[BvU]

Let's ask @haruspex for a hint ..

 

[haruspex]

This answer is incorrect when I try submitting it.

Your answer looks right to me, but…
What would your answer be if all the wires were length L? Would you expect the result to be the same for both scenarios?
I am not at all sure… just asking.

 

[risakapal]

The answer worked! It seems I did not need a subscript for the constant. Thank you very much for your help!