When will two current-carrying wires touch each other

In summary, the conversation discusses determining where and when two parallel wires, with a current of 10 A and a mass of 2.5 g each, will touch each other. The force between the wires is calculated using the equations for magnetic flux density and force, and it is assumed that the force is constant throughout. After considering the distance and time, it is determined that the wires will touch each other at half the distance between them and the time can be calculated using the distance and velocity equations. However, the use of differential equations is suggested for a more accurate solution. The method provided in the conversation is deemed to be correct.
  • #1
Asmaa Mohammad
182
7

Homework Statement


Two wires are free to move, the current in each one is 10 A, the mass of each one is 2.5 g, they are separated by a distance of 20 cm, and the length of each one is 5 cm.
Determine (i) where and (ii) when will the two wire touch each other if they were standing parallel to each other.

Homework Equations


1. B=μi/2πd
2. F= Bil
3. F (interchangeable between two wires) =μi₁i₂l/2πd
4. a= Δv/t = Δx/t²

(Where: B is the magnetic flux density, i is the current, F is the force, a is the acceleration, v is the velocity, x is the distance and t is the time.)

The Attempt at a Solution


[/B]
(i) where will they touch each other?
Since the direction of the current is not mentioned in the problem statement, I assumed that the current in both wires would be in the same direction so that they can attract each other.
And since the current in both wires is 10A, and it flows in the same direction, they will touch each other at half the distance between the wires (at point y in Figure below).

(ii) when will they touch each other?
That's my attempt to determine the time they reach point y.
5mejC.jpg

Note: Δx= 0.1-0=0.1 =x.
(Ia and Ib) are (i₁ and i₂).
So, is my attempt correct?
 
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  • #2
Have you studied calculus?
The force is not constant throughout. You need to use differential equations.
 
  • #3
cnh1995 said:
Have you studied calculus?
The force is not constant throughout. You need to use differential equations.
Which differential equations? Clarify please!
 
  • #4
Asmaa Mohammad said:
Which differential equations? Clarify please!
I gather you are a high school student from your profile. I now doubt that you are supposed to use DEs. Have you formally studied calculus? What is the provided answer?

Maybe you should just assume the force to be constant.
 
  • #5
cnh1995 said:
I gather you are a high school student from your profile. I now doubt that you are supposed to use DEs. Have you formally studied calculus? What is the provided answer?

Maybe you should just assume the force to be constant.
I studied calculus two years ago. This year I only have physics, chemistry, biology and geology. I remember only a small bit of information about differential equations, because I don't use them in my physics course this year.
There is no a provided answer unfortunately.
And yes, I guess I should assume that the force is constant. So, how would be my attempt at solution putting those points into consideration.
 
  • #6
cnh1995 said:
Have you studied calculus?
The force is not constant throughout. You need to use differential equations.
Scratch that!
(Even I'm not sure if I can solve it using DEs o:)).

Asmaa Mohammad said:
So, how would be my attempt at solution putting those points into consideration.
I didn't check the numbers but your method looks good to me.
 
  • #7
cnh1995 said:
Scratch that!
(Even I'm not sure if I can solve it using DEs o:)).I didn't check the numbers but your method looks good to me.
Looks?! But, cnh1995, I depend on your help to pass my physics exam this year :biggrin::biggrin:. I have no teacher and that problem confused me, could you check the numbers, please, and give me the final word.
Thanks in advance:smile::smile:
 
Last edited:
  • #8
Asmaa Mohammad said:
Looks?! But, cnh1995, I depend on your help to pass my physics exam this year :biggrin::biggrin:. I have no teacher and this problem confused me, could you check the numbers, please, and give me the final word.
Thanks in advance:smile::smile:
I am getting the same answers.
 
  • #9
Ok, thank you very much!
 
  • #10
Asmaa Mohammad said:
Ok, thank you very much!
You're welcome!
 

Related to When will two current-carrying wires touch each other

1. What is the likelihood of two current-carrying wires touching each other?

The likelihood of two current-carrying wires touching each other depends on several factors, including the distance between the wires, the strength of the current, and the materials of the wires. In most cases, it is unlikely for two wires to touch each other unless they are intentionally crossed or come into close proximity due to external forces.

2. What happens when two current-carrying wires touch each other?

When two current-carrying wires touch each other, it can create a short circuit. This means that the current will take the path of least resistance and flow through the point of contact between the two wires. This can cause a sudden increase in current, potentially leading to damage or overheating of the wires.

3. How can I prevent two current-carrying wires from touching each other?

To prevent two current-carrying wires from touching each other, it is important to properly insulate and secure the wires. This can be done using electrical tape, wire connectors, or other insulating materials. It is also important to plan and organize the placement of wires to minimize the chances of them coming into contact with each other.

4. Can two current-carrying wires touch each other safely?

In most cases, it is not safe for two current-carrying wires to touch each other. As mentioned earlier, it can create a short circuit and potentially lead to damage or overheating. However, there are some instances where two wires may touch safely, such as in a properly designed circuit or when the wires are specifically designed for contact with each other.

5. What are the potential risks of two current-carrying wires touching each other?

The potential risks of two current-carrying wires touching each other include creating a short circuit, overheating and potentially causing a fire, damaging the wires and other components in the circuit, and creating a safety hazard for anyone nearby. It is important to take precautions to prevent wires from touching and to handle any contact carefully to avoid these risks.

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