Solve Magnetism Problem: Find Direction, Magnitude of Force

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In summary, the problem involves two wires suspended from the ceiling with a current running through each. One wire has an angle of β with the vertical and the other an angle of θ. The goal is to find the direction of the current in the wires, the magnitude of the magnetic force between them, and the magnitude of the magnetic force in each wire. The equations needed are the current carrying wire in a magnetic field, the magnetic field due to a current carrying wire, and the magnetic force between two current carrying wires. The two wires appear to be attracting each other, and in order for this to occur, they must be pointing in the same direction. The diagram shows that they are not touching, so the distance between them cannot be set
  • #1
doodijh
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Homework Statement


Two wires have a current going through them and each wire is suspended by a string from the ceiling.
Wire 2 makes an angle of β with the vertical and Wire 1 makes and angle of θ with the vertical.
(see the attached picture for further clarification)

L 1(length of wire) = ?
I 1(current) = ?
L 2(length of wire) = ?
I 2(current) = ?
B (magnetic field) =?
D (distance in between the two wires) =?
M1 (mass of wire 1) = ?
M2 = ?
Fm = ?

a) Find the direction of current in the two wires?
b) State the magnitude of the magnetic force between the two wires (1&2)?
c) Find the magnitude of the magnetic force in each wire?



Homework Equations



Current carrying wire in a magnetic field
latex2png.2.php?z=100&eq=F_m%20%3D%20IlBsin%5Ctheta.jpg

Magnetic field due to current carrying wire
latex2png.2.php?z=100&eq=B%20%3D%20u_0%20(%5Cfrac%7BI%7D%7B2%5Cpi(r)%7D).jpg

Magnetic force between two current carrying wires
latex2png.2.php?z=100&eq=F_m%20%3D%20%5Cfrac%7Bu_0I_1%20I_2%7D%7B2%5Cpi(r)%7D%20.jpg


[tex]\mi_{o}\ =\ 4\pi\ \times\ 10^{-7}[/tex]

The Attempt at a Solution


a) the two wires seem to be attracting each other because if they were repulsive, then their angles from the vertical must be the same. According to the right hand rule, the two wires have to point in the same direction in order to have an attractive force with each other.

b&c) I had no idea of how to do them. I just wrote the appropriate equation beneath the letters. This question was the last question from my test in magnetism (by the way I am a grade 12 university student)

If I get the test back, then I will post the solution to this problem, but I would like to see how u people would solve this problem.
 

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  • #2
by the way the constant was U0
 
  • #3
Your diagram is so small as to be practically illegible. Could you post a zoomed-in version at higher resolution (and without all that extra space around it)?
 
  • #4
diazona said:
Your diagram is so small as to be practically illegible. Could you post a zoomed-in version at higher resolution (and without all that extra space around it)?

ok.
In my new image, imagine the roof as if it was tilted.
& the space around it has nothing to do with the solution of
the problem.
 
  • #5
doodijh said:

The Attempt at a Solution


a) the two wires seem to be attracting each other because if they were repulsive, then their angles from the vertical must be the same. According to the right hand rule, the two wires have to point in the same direction in order to have an attractive force with each other.
Think about this: if they are attracting each other, what's preventing them from coming all the way together and touching?
 
  • #6
diazona said:
Think about this: if they are attracting each other, what's preventing them from coming all the way together and touching?

First, it will be absurd to ask in b) of the magnetic force in between them and then set the distance between them as zero (that's what happen when the 2 wires touch each other) If the distance between them is zero, then the equation of the magnetic force will not work.

Second, the angle of theta is bigger than beta, making it obvious that one wire is clearly getting attracted to the other.

Finally, you can not set a picture of two wires attached to each other -> refer back to my first and second reason.

cool :smile:
 
  • #7
doodijh said:
First, it will be absurd to ask in b) of the magnetic force in between them and then set the distance between them as zero (that's what happen when the 2 wires touch each other) If the distance between them is zero, then the equation of the magnetic force will not work.
That's true, but the diagram shows you that they are clearly not touching. So that's not a concern.

doodijh said:
Second, the angle of theta is bigger than beta, making it obvious that one wire is clearly getting attracted to the other.
Not only is it not obvious, it is wrong. I don't understand how you are coming to that conclusion.

I was asking, if the wires are attracting each other, why is it not the case that [itex]\theta + \beta = 0[/itex]? Think about this: if there were no current in these wires and gravity were the only force involved, it would be true that [itex]\theta + \beta = 0[/itex], since both wires would be hanging straight down. Agreed? Now, as the diagram shows, that is clearly not the case. Something is working against gravity. What kind of force between the wires could do that - attractive or repulsive?
 
  • #8
diazona said:
That's true, but the diagram shows you that they are clearly not touching. So that's not a concern.


Not only is it not obvious, it is wrong. I don't understand how you are coming to that conclusion.

I was asking, if the wires are attracting each other, why is it not the case that [itex]\theta + \beta = 0[/itex]? Think about this: if there were no current in these wires and gravity were the only force involved, it would be true that [itex]\theta + \beta = 0[/itex], since both wires would be hanging straight down. Agreed? Yes

Now, as the diagram shows, that is clearly not the case. Something is working against gravity. What kind of force between the wires could do that - attractive or repulsive?

I think the picture was taken the instant the wires were released, and so u don't know whether the wires will collide or be repellisive to each other. However, you can assume that if one angle is greater than the other then the wire with less angle is the one being attracted, meaning that there is an attractive force between each other. If the two wire were repulsive to each other, then theta and beta will be the same in magnitude.

You thought that the diagram was taken after the wires were released, but I think that the diagram represent an instanteous release of the two wires.
 
  • #9
Why do you assume this? You may be right, but say that the current through one of the loops is much greater than that thru the other. The resultant magnetic field will be much greater in the one case than the other. Now it may the force "felt" by each of the loops will be the same, but I don't see that you have shown that. The other part of this problem that is difficult, is that as the angles change so too will be the magnitude of the cross product, not just because of distance but deviation from right angles of the interacting fields.

Besides, just because the two angles are depicted with different symbols doesn't mean they are different. It may just be a fake out. Altogether a challenging problem for G12.
 

Related to Solve Magnetism Problem: Find Direction, Magnitude of Force

1. What is magnetism and how does it affect the force of an object?

Magnetism is a physical phenomenon in which certain materials have the ability to attract or repel other materials. When an object with a magnetic field interacts with another object, it can cause a force to be exerted on that object, either attracting or repelling it depending on the orientation of the magnetic fields.

2. How do you determine the direction of the magnetic force on an object?

The direction of the magnetic force on an object can be determined by using the right hand rule. Point your thumb in the direction of the object's velocity, your fingers in the direction of the magnetic field, and the direction in which your palm is facing will be the direction of the magnetic force.

3. How do you calculate the magnitude of the magnetic force on an object?

The magnitude of the magnetic force can be calculated using the formula F = qvBsinθ, where q is the charge of the object, v is its velocity, B is the strength of the magnetic field, and θ is the angle between the velocity and the magnetic field.

4. Can the direction and magnitude of the magnetic force change?

Yes, the direction and magnitude of the magnetic force can change if there is a change in any of the variables in the formula. This includes changes in the charge or velocity of the object, the strength or direction of the magnetic field, or the angle between the velocity and the magnetic field.

5. What are some real-world applications of solving magnetism problems?

Solving magnetism problems is important in a variety of fields, including engineering, physics, and geology. Some real-world applications include designing and building electromagnets, understanding the magnetic fields of the Earth and other planets, and developing magnetic levitation technology for transportation systems.

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