Magnetic Force Between Wires Problem #2

[medgirl]

I'm sorry to post two questions in succession, this is another one on the same topic (I'm obviously having trouble with this whole concept for some reason...)

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 8.00 A, but its direction in wire A (at the top of the triangle) is opposite to that in wires B and C (the bottom points of the triangle). A comes out of the page, while B and C go into the page. Determine the magnetic force per unit length on each wire due to the other two, and the angle of each force.

Homework Equations

F/l = [u (2I)]/[2pi (d)]

The Attempt at a Solution

I can plug into the above equation to find 2.96e-5 N/m. Is this the force for all of the three points? For some reason, the solutions I have indicate that wire A has a different force (5.13e-5 N/m) and I'm not sure why. I am also very unsure how to determine the angles at which these forces point. Is this a vectors problem? I feel like I am missing some pieces of information and I am not sure how to put together what I know to solve this. I'm sorry that this attempt at a solution is so vague...
Again, I would really appreciate some insight!

 

[Born2bwire]

Yes. The force will always have an associated direction. You need to find the direction and magnitude of each force and add them together as vectors to find the total force and its direction. If I have two guys that can pull on a rope each with a force of 5 N, it matters what direction I set the two men to pull a crate. If I put them on the same side of the crate they can pull together with a net force of 10 N. If I put them on opposite sides of the crate they will pull against each other for a net force of 0 N.

 

[nlightner]

Dear student,

Thank you for posting your question. It is completely normal to have difficulty with certain concepts in science, so do not worry. Let's break down the problem and see if we can find the missing pieces of information.

First, let's look at the equation you have used to calculate the magnetic force per unit length (F/l). This equation, also known as Ampere's law, gives the total magnetic force per unit length on a wire due to a current-carrying wire. However, in this problem, we have three wires and we need to calculate the force on each individual wire.

To do this, we can use the principle of superposition, which states that the total force on an object is the sum of the individual forces acting on it. In this case, the total force on each wire will be the sum of the forces due to the other two wires.

Now, let's look at the direction of the forces. Since all three wires are parallel, the forces between them will be attractive or repulsive depending on the direction of the current. In this problem, wire A has an opposite direction of current compared to wires B and C, so the forces between them will be repulsive. This means that the force on wire A will be in the opposite direction compared to the forces on wires B and C.

To determine the angle of the forces, we can use the right-hand rule. If you curl your fingers in the direction of the current in wire A, your thumb will point in the direction of the force on wire A. Similarly, if you curl your fingers in the direction of the current in wires B and C, your thumb will point in the direction of the forces on wires B and C. This will give you the direction of the forces and the angles at which they act.

I hope this helps you understand the problem better and find the missing pieces of information. Keep practicing and don't hesitate to ask for help if you need it. Good luck!