Calculating a Magnetic Force Concerning Paralell Wires

[PeachBanana]

Homework Statement

Three long parallel wires are 3.8 cm from one another. (Looking along them, they are at three corners of an equilateral triangle.) The current in each wire is 5.30 A , but its direction in wire M is opposite to that in wires N and P (see the figure).

1. Determine the magnitude of the magnetic force per unit length on wire M due to the other two.
2. Determine the angle of the magnetic force per unit length on wire M due to the other two.

Homework Equations

F = μI1I2/ 2∏d

The Attempt at a Solution

1. F = (1.256*10^-6 NA^-2)(5.30 A)(5.30 A) / (2∏) (0.038 m)

F = 1.474*10^-4 N

2. Does it make sense to you all if I used the fact:

B = F / Il

then did sin (F / Ilb) ^ -1 = θ for each wire, then take the summation of the θs?

 

[anathema]

Thank you for your interesting question! Based on the given information and equations, it seems like you are on the right track in solving for the magnetic force per unit length on wire M. However, there may be a simpler way to approach the problem.

First, let's define some variables to make our calculations easier. Let's say wire N is on the left, wire P is on the right, and wire M is in the middle. We can also label their distances from wire M as dN and dP, respectively.

Now, to find the magnetic force per unit length on wire M, we can use the equation F = μI1I2/ 2∏d, but instead of using the full distances of 0.038 m, we can use the distances between each wire, which is 0.038/2 = 0.019 m. This is because we are only interested in the force between each individual wire and wire M, not the total force between all three wires.

So, for wire N, the force per unit length would be:

F_N = (1.256*10^-6 NA^-2)(5.30 A)(5.30 A) / (2∏) (0.019 m) = 3.685*10^-4 N/m

And for wire P, the force per unit length would be:

F_P = (1.256*10^-6 NA^-2)(5.30 A)(5.30 A) / (2∏) (0.019 m) = 3.685*10^-4 N/m

Since the current in wire M is in the opposite direction, the total force per unit length on wire M would be the difference between these two forces:

F_M = F_N - F_P = 3.685*10^-4 N/m - 3.685*10^-4 N/m = 0 N/m

This means that the magnetic force per unit length on wire M due to the other two wires is zero. This makes sense because the forces from wires N and P would cancel each other out due to their opposite directions.

Now, for the angle of the magnetic force per unit length on wire M, we can use the fact that the force is perpendicular to the wire and the magnetic field, which is in the direction of the current. So, the angle would be 90 degrees, or π/2