How Does Current Direction Affect Torque in Parallel Wires?

[syhpui2]

Homework Statement

http://i.imgur.com/EHokd.png

Two long wires carry currents I1 and I2 as shown in the figure. The first wire runs parallel to the x-axis but is a distance d above the x-y plane. The second wire lies along the y-axis and passes through the origin.
What is the direction of the torque on the wire carrying I1 due to the current I2 in the other wire?
(a) in the positive y direction
(b) in the positive z direction Correct Answer
(c) in the negative y direction

Homework Equations

F=BI X L

The Attempt at a Solution

I first use Ampere's law to find magnetic field caused by I2 which is counterclockwise.
However, then how should I use RHR to determine force direction? How about torque direction? Is torque direction just used RHR for force and distance torqure= Fd?
Is there any difference if instead I use RHR from I to B or B to I?

Thanks!

 

[anathema]

Thank you for your question. To determine the direction of the torque on the wire carrying I1 due to the current I2 in the other wire, you can use the right hand rule for cross products. The direction of the torque can be determined by the direction of the magnetic field (B), the current (I1), and the distance between the two wires (d). The formula for torque is T = I1 x B x d, where x represents the cross product.

To use the right hand rule, you can point your thumb in the direction of the current I1, your index finger in the direction of the magnetic field B, and your middle finger in the direction of the distance between the two wires (d). The direction that your middle finger points represents the direction of the torque.

In this case, since the current I2 is flowing in the y-direction, the magnetic field B will be in the positive z-direction (using the right hand rule for magnetic fields around a wire). Therefore, the torque will be in the direction of your middle finger, which is in the positive z-direction. This means that the correct answer is (b) in the positive z-direction.

I hope this helps. Please let me know if you have any further questions.