Magnetic force on wires -direction of B

In summary, to determine the current needed for a third wire to form an equilateral triangle with two other wires, we can use the equation F=IlBsin(theta) to calculate the force on the current carrying wire. By considering the magnetic field and forces separately, we can arrive at two different answers. The 60 degree angle in the equation comes from the fact that the bottom wires create a magnetic field at an angle of 60 degrees to the horizontal.
  • #1
bcjochim07
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0

Homework Statement


Three wires have linear density of 50 g/m. They each carry the same current. The bottom two are 4 cm apart and carry currents into the page. What current I will allow the third wire to float so as to form an equilateral triangle with the other two?


Homework Equations





The Attempt at a Solution


I think I am really close, but I'm just concerned because I'm having some problems with magnetic field directions and components.

If I start with the magnetic field, I think that the y- components of the magnetic fields of the bottom two wires cancel. So the net B-field is:

2* cos(60) * (1.257*10-6)I / 2pi*.04 = (5*10^-6)I

F=IlBsin(theta) for the force on a current carrying wire

F= I^2 * (5*10-6) * l = (9.8)(.05)*l
I= 313A.

This isn't quite correct, however, I find that if I turn to forces first, and seeing that the bottom two have forces where the x-components cancel.

F = I^2 * l * (5*10-6)*sin(60) = .05*9.8l
I = 237 A This is correct. But I am confused by why the two give different answers.
 
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  • #2
bcjochim07 said:
2* cos(60) * (1.257*10-6)I / 2pi*.04 = (5*10^-6)I

Where does the cos(60) come from?
 
  • #3
Isn't the magnetic fields from the bottom wires at an angle of 60 degrees to horizontal? So with cos(60) I am getting the x components from those mag. fields and adding them together.
 
  • #4
bcjochim07 said:
Isn't the magnetic fields from the bottom wires at an angle of 60 degrees to horizontal?

I'm getting that B is 60 degrees from vertical.
 

1. What is the direction of the magnetic force on a wire?

The direction of the magnetic force on a wire depends on the direction of the current and the direction of the magnetic field. The force is perpendicular to both the current and the magnetic field, following the right-hand rule.

2. How do I determine the direction of the magnetic field around a wire?

The direction of the magnetic field around a wire can be determined using the right-hand rule. Point your thumb in the direction of the current, and your fingers will curl in the direction of the magnetic field.

3. Does the magnetic force on a wire change with the strength of the current?

Yes, the magnetic force on a wire is directly proportional to the strength of the current. As the current increases, the force also increases.

4. Can the direction of the magnetic force on a wire be reversed?

Yes, the direction of the magnetic force on a wire can be reversed by changing the direction of either the current or the magnetic field.

5. How does the length of the wire affect the magnetic force?

The length of the wire does not affect the magnetic force on the wire. The force is only dependent on the strength of the current and the strength of the magnetic field.

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