The figure below shows three parallel wires arranged in a equilateral triangle w

Question

The figure below shows three parallel wires arranged in a equilateral triangle with sides of length 10.0 cm. The wire at the apex carries a current of 6.0 A and points out of the page while the two wires at the bottom has currents of 10.0 A and 21.0 A pointing into the page.

1/ Find the magnitude of the force on the wire at the top apex due to the other two wires using vector addition. (in N)

2/ Find the direction of the force that on the wire at the top apex due to the other two wires. Specify the angle from the +x-axis going counter-clockwise (see figure on right). (in deg)

3/ Find the magnitude of the force on the bottom left wire due to the other two wires using vector addition. (in N)

4/ Find the direction of the force that on the bottom left wire due to the other two wires. Specify the angle from the +x-axis going counter-clockwise (see figure on right). (in deg)

5/ Find the magnitude of the force on the bottom right wire due to the other two wires using vector addition. (in N)

6/ Find the direction of the force that on the bottom right wire due to the other two wires. Specify the angle from the +x-axis going counter-clockwise (see figure on right). (in deg)

Explanation / Answer

So each case has 2-4 wires with varying currents and distances between; I have to calculate the magnetic force and then rank all of the wires by magnitude. For example, the 1st one looks like:

Wire A: ----->-----3A
Wire B: ----->-----2A

Wire C: ----->-----6A

Distance from Wire A to Wire B = d
Distance from Wire B to Wire C = 2d (and from A to C is 3d obviously).

Using Ampere's Law, I calculated Wire A's magnitude to be 12A/d, which is correct.

I found Wire B = -12A/d which is wrong, the correct answer is 0. Apparently the force vectors cancel out but I thought they should be added.

Ok, so then would I subtract the magnetic force between A/B from B/C to get the total magnetic force on B? As in:

F/L = ?/2? (2A x 6A/2d) - (2A x 3A/d) = 0

And then would C = -12A/d?

As shown at the Hyperphysics page (and in your textbook), the force on second wire due to the current in a first wire is proportional to the current in the first wire, and inversely proportional to the separation distance.

So add up the two forces from the currents in Wires A and B to get their effect on C. What is the current in Wire A? How far is it away from Wire C? What is the current in Wire B? How far is it away from Wire C? Add up those two quantities to get the relative force (the question appears to be asking for the relative magnitudes of the forces on each wire due to the others, so the other terms in the force equation cancel out, except for the currents and separation distances....)

I don't get how to apply the right hand rule to get the force one wire has on another, and then how to use that in Ampere's Law to calculate the magnetic force between the wires.

For example, in this problem:

Wire 1 ------>-------3A
Wire 2 ------<--------2A
Wire 3 ------>--------6A

Now the forces are 0 on all three wires, but why

The distance between Wire 1 and 2 is d. The distance from Wire 1 and 3 is 3d. And the distance from Wire 2 and 3 is 2d.

So for Wire 3, I did:

(6A x 2A)/2d + (6A x 3A)/3d = 12A/d

But the answer is 0, so the force between Wires 2/3 must be subtracted from the force between Wires 1/3 like this:

(6A x 2A)/2d - (6A x 3A)/3d = 0

I don't know why the force is subtracted here (I think I must be using the right hand rule wrong if I'm adding rather than subtracting forces).

For the first term: (6A x 2A)/2d wrap your right hand around Wire 2 with your thumb pointing left in the direction of the current. Your fingers touch Wire 3 with your fingertips pointing toward you.

For the second term: (6A x 3A)/3d wrap your right hand around Wire 1 with your thumb pointing right in the direction of the current. Your fingers touch Wire 3 with your fingertips pointing away from you.

So for however you set up your x-y-z coordinates, the vectors you get for those two terms will point opposite directions, and will subtract.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects