How Does Current Affect the Magnetic Force Between Two Wires?

[skye204]

Homework Statement

Two straight wire are suspended from the ceiling by strings length of 0.75m.
each wire has a mass of 45g and a length of 1m
When identical current flows in opposite directions, the angle between the string is 12°.

Homework Equations

Fg=mg
B=μI/2πR
F=LIBsin(theta)

The Attempt at a Solution

From the looks of it, I assumed that this was an equilibrium question meaning that the force of (BIL) is the same on both wires, working in opposite directions to create an angle of 12°.
I also assumed that the force of gravity (.441) is equal to the Y component of the string, so then i used trig to solve for the force of the X component which i found to be .0464.

The force of the X component is the same force as the (BIL) and in order for the forces to be the same, the magnetic field and current has to be the same.

so then i combined B=μI/2πR with F=LIBsin(theta) in order to cancel out the magnetic Field since it did not matter.

I got F= LμI²/2πR

I figured out the current to be 131.9

I would attach a picture of my work but i don't have 10 post..
imageshack.us/photo/my-images/265/photo20120607121104pm.jpg/

 

[anathema]

Hello,

Your approach to this problem seems to be on the right track. However, I do have a few suggestions for improvement.

First, when using trigonometry to solve for the X-component of the force, make sure you are using the correct angle. In this case, the angle of 12° is the angle between the strings, not the angle between the force and the string. To find the angle between the force and the string, you can use the fact that the force and the string form a right triangle, and the angle between them is the complementary angle to the angle between the strings.

Secondly, when combining the equations F=LIBsin(theta) and B=μI/2πR, make sure you are using the correct value for the length of the wire. In this case, the length of the wire is given as 1m, not 0.75m. Also, you can use the value of the X-component of the force that you found earlier to solve for the current, instead of solving for the force again.

Finally, when solving for the current, make sure you are using the correct units. The equation B=μI/2πR should give you a value in Tesla (T), so make sure to convert the units of the permeability constant (μ) accordingly.

Overall, your approach to solving this problem is sound. Just make sure to double check your calculations and units to ensure accuracy. Keep up the good work!