Calculating Fx of Three Parallel Wires

[kjlchem]

Homework Statement

Three infinite straight wires are fixed in place and aligned parallel to the z-axis as shown. The wire at (x,y) = (-21 cm, 0) carries current I1 = 2 A in the negative z-direction. The wire at (x,y) = (21 cm, 0) carries current I2 = 1 A in the positive z-direction. The wire at (x,y) = (0, 36.4 cm) carries current I3 = 5.8 A in the positive z-direction.

What is Fx(1), the x-component of the force exerted on a one meter length of the wire carrying current I1?

Homework Equations

(1) F = IL x B

(2) B= μI/2∏R

The Attempt at a Solution

I found that B of 2 on 1 is 4.76*10^-7 T and B of 3 on 1 is 5.524*10^-6 T using equation 2. I think that B (2,1) is in the negative vertical direction, and that B (3,1) is pointed 60° S of the x axis. So, to find the y components of both (the x component of the F, the only thing I need to do is multiply B (3,1) times the sine of 60 and then I can use equation 1 to give me the force. Unfortunately, this is not correct. I don't understand what I am doing wrong.

 

[anathema]

Thank you for your post. It seems like you have correctly calculated the magnetic fields at the locations of the wires. However, your approach for finding the force on wire 1 is incorrect. The force on a wire due to a magnetic field is given by the equation F = I x B, where I is the current in the wire and B is the magnetic field. This equation is a vector equation, meaning that the force is also a vector quantity with both magnitude and direction.

To find the x-component of the force on wire 1, you need to take the cross product of the current in wire 1 with the magnetic field at its location. This will give you a vector with both x and y components, and the x-component will be the one you are looking for.

In this case, the current in wire 1 is in the negative z-direction, so its vector representation is I1 = 0i - 0j - 2k. The magnetic field at its location is in the negative y-direction, so its vector representation is B1 = 0i - 4.76*10^-7j + 0k. Taking the cross product of these two vectors, you will get a vector with components in all three directions. However, the x-component is the one you are interested in, and it will be given by the product of the y-components of the two vectors, which is 2 x 4.76*10^-7 = 9.52*10^-7 N.

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