Magnetic forces on current-carrying wires

AI Thread Summary
The discussion centers on understanding the magnetic forces acting on a current-carrying wire (wire X) due to two other wires (Y and Z). The resultant force per unit length on wire X is given as 0.5 mN/m, which is influenced by the contributions from wires Y and Z. There is confusion regarding the direction of the forces, particularly the phrase "towards X," which participants find unclear. It is clarified that the direction of the forces must be perpendicular to wire X, and calculations reveal that the force from wire Y is to the left while the force from wire Z must be determined to achieve the resultant force. Ultimately, the direction of the current in wire Z is concluded to be downward to align with the established forces.
hooman
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Homework Statement
Three long straight thin conductors X, Y, Z lie on the same plane and are parallel to each
other as shown in Figure 1.Current flows in each conductor in the direction as shown. The
earth’s magnetic field may be neglected. The resultant magnetic force per unit length acting
on X is 0.50 mN m-1 , pointing towards X.
a) Is the direction of the current in Z shown in the diagram correct? Explain.
b) Determine the current in Z.
Relevant Equations
F/l= 0.50
please correct me if I'm wrong.

is it for the question b, F/l= 0.50 right? does that mean the resultant magnetic force at X is determine by the force at Y and Z? do I need to consider the direction to solve the equation? first step to know the direction of each conductors I use the right hand rule and I already get the direction of the forces for each conductors then I don't know whether I need to consider the direction like positive or negative to put in the equation. Please help me, thank you.
 

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hooman said:
is it for the question b, F/l= 0.50 right?
That's given as the force per unit length acting on wire X. Although I am not sure what "pointing towards X" means. (What's the direction of the force on X? up, down, left, right, into the page, out of the page?)
hooman said:
does that mean the resultant magnetic force at X is determine by the force at Y and Z?
The resultant force on X is due to the magnetic fields from Y and Z that act on X.
 
Doc Al said:
That's given as the force per unit length acting on wire X. Although I am not sure what "pointing towards X" means. (What's the direction of the force on X? up, down, left, right, into the page, out of the page?)

The resultant force on X is due to the magnetic fields from Y and Z that act on X.
direction force of X is to the left
 
hooman said:
direction force of X is to the left
That's what I assumed they meant. (But that could have been stated more clearly.)

So, what's the force per length on X due to the current in Y?
 
Doc Al said:
That's what I assumed they meant. (But that could have been stated more clearly.)

So, what's the force per length on X due to the current in Y?
you mean the value or what?
 
hooman said:
you mean the value or what?
Yes. Magnitude and direction.
 
Doc Al said:
Yes. Magnitude and direction.
2.5x10^-4 , direction to the left
 
hooman said:
2.5x10^-4 , direction to the left
So what additional force must wire Z exert on X to produce the given resultant?
 
hooman said:
The resultant magnetic force per unit length acting
on X is 0.50 mN m-1 , pointing towards X.
I find this statement confusing (not your fault). The magnetic force per unit length acting on wire X must be perpendicular to the wire marked X. As such, the force must point either away from wire Y (or Z) or towards it. "Towards X" makes no sense to me. Regardless of this, how do you propose to approach the problem if the direction of the force on X were given to you in a way that makes sense?
 
  • #10
Doc Al said:
So what additional force must wire Z exert on X to produce the given resultant?
is it 0.49975 ?
 
  • #11
kuruman said:
I find this statement confusing (not your fault). The magnetic force per unit length acting on wire X must be perpendicular to the wire marked X. As such, the force must point either away from wire Y (or Z) or towards it. "Towards X" makes no sense to me. Regardless of this, how do you propose to approach the problem if the direction of the force on X were given to you in a way that makes sense?
i would consider the direction of force is away from Y
 
  • #12
hooman said:
is it 0.49975 ?
Note that the resultant (total) force/length on X is given as 0.5 mN/m = 0.5 10^(-3) N/m.
 
  • #13
kuruman said:
I find this statement confusing (not your fault). The magnetic force per unit length acting on wire X must be perpendicular to the wire marked X. As such, the force must point either away from wire Y (or Z) or towards it. "Towards X" makes no sense to me. Regardless of this, how do you propose to approach the problem if the direction of the force on X were given to you in a way that makes sense?
I agree with your comments about the confusing wording of the direction of the force. I wonder what book this is from? (The best I could assume is that they meant from Y or Z toward X. Not clear at all.)
 
  • #14
Doc Al said:
I agree with your comments about the confusing wording of the direction of the force. I wonder what book this is from? (The best I could assume is that they meant from Y or Z toward X. Not clear at all.)
Another interpretation might be "towards the positive x-axis", i.e. to the right.
 
  • #15
kuruman said:
Another interpretation might be "towards the positive x-axis", i.e. to the right.
Indeed!
 
  • #16
Doc Al said:
Note that the resultant (total) force/length on X is given as 0.5 mN/m = 0.5 10^(-3) N/m.
i see, i thought the m here is metre. so i mistaken here. that's why when i do the solution i find it weird
 
  • #17
Doc Al said:
I agree with your comments about the confusing wording of the direction of the force. I wonder what book this is from? (The best I could assume is that they meant from Y or Z toward X. Not clear at all.)
this is my assignment's question
 
  • #18
Doc Al said:
Note that the resultant (total) force/length on X is given as 0.5 mN/m = 0.5 10^(-3) N/m.
so that means that resultant F/l is the sum of F/l from Y and from Z right?
 
  • #19
hooman said:
so that means that resultant F/l is the sum of F/l from Y and from Z right?
Correct.
 
  • #20
hooman said:
this is my assignment's question
Yes, it is that. However it's like giving you the equation ##y = 3 + x## and asking you to find ##x## given that the absolute value of ##y## is 5. There are two answers.
 
  • #21
Doc Al said:
Correct.
the question a , it ask for the direction of current Z correct or not. how to know it?
 
  • #22
hooman said:
the question a , it ask for the direction of current Z correct or not. how to know it?
If you know how much F/l wire Z must contribute, then you can figure out what direction its current must have.
 
  • #23
Doc Al said:
If you know how much F/l wire Z must contribute, then you can figure out what direction its current must have.
the F/l wire Z is 2.5x10^-4 also. the direction is correct?
 
  • #24
kuruman said:
Yes, it is that. However it's like giving you the equation ##y = 3 + x## and asking you to find ##x## given that the absolute value of ##y## is 5. There are two answers.
the question a , it ask for the direction of current Z correct or not. how to know it?
 
  • #25
hooman said:
the question a , it ask for the direction of current Z correct or not. how to know it?
That is what it is asking. To know the direction of the current, you need to know the direction of the force on wire X. This direction could be to the left or to the right. The statement of the problem says "towards X" which is neither to the left nor to the right.
 
  • #26
All about working out the force from each wire on X, the you know which way the current should be..
 

Attachments

  • #27
kuruman said:
That is what it is asking. To know the direction of the current, you need to know the direction of the force on wire X. This direction could be to the left or to the right. The statement of the problem says "towards X" which is neither to the left nor to the right.
do you think it make sense if I said the "towards X" in the statement means the direction of force on X by Z? because it is impossible for the force on X by Y to be towards X as the current is in different direction. what do you think?
 
  • #28
hooman said:
do you think it make sense if I said the "towards X" in the statement means the direction of force on X by Z? because it is impossible for the force on X by Y to be towards X as the current is in different direction. what do you think?
No, it does not mean the direction of force on X by Z. The problem states clearly that it is the resultant on X, that is the sum of forces by Y and Z.
 
  • #29
MartinCarr said:
All about working out the force from each wire on X, the you know which way the current should be..
so, you minus the Fy and Fz because it is in different direction? what do you mean by the 2 current must in opposite direction? which current that you mean? X and Y or X and Z?
 
  • #30
See the attached file on the above post..
 
  • #31
MartinCarr said:
See the attached file on the above post..
i've already seen it but i don't understand. can you please explain it to me based on the question i asked above.
 
  • #32
How about answering the question I posed earlier?
Doc Al said:
So what additional force must wire Z exert on X to produce the given resultant?
You are given the resultant F/L on wire X. You've calculated the contribution from wire Y. So, what must be the contribution from wire Z? That will tell you the direction of the current in Z and allow you to calculate the magnitude of that current.
 
  • #33
Doc Al said:
How about answering the question I posed earlier?

You are given the resultant F/L on wire X. You've calculated the contribution from wire Y. So, what must be the contribution from wire Z? That will tell you the direction of the current in Z and allow you to calculate the magnitude of that current.
2.5x10^-4 . is it right?
 
  • #34
Did you work this out or do you need me to explain more?
 
  • #35
hooman said:
2.5x10^-4 . is it right?
Don't just give a numeric answer. Describe how you got your answer. And what does that tell you about the direction and magnitude of the current through Z?
 
  • #36
MartinCarr said:
Did you work this out or do you need me to explain more?
explain please
 
  • #37
Doc Al said:
Don't just give a numeric answer. Describe how you got your answer. And what does that tell you about the direction and magnitude of the current through Z?
from the question a, i need to know the direction whether it is right or wrong. so, fron the diagram itself we can know whether it is right or wrong. but i don't know how. i cannot determine the direction by using calculation because how can i know the equation have to use minus or addition.
 
  • #38
MartinCarr said:
Did you work this out or do you need me to explain more?
the statement is wrong. the right one is the resultant force per unit length is actually acted on Y not on X. it's a mistake in typing the question. sorry. so how to determine the direction whether it's right or wrong?
 
  • #39
Doc Al said:
Don't just give a numeric answer. Describe how you got your answer. And what does that tell you about the direction and magnitude of the current through Z?
the statement is wrong. the right one is the resultant force per unit length is actually acted on Y not on X. it's a mistake in typing the question. sorry. so how to determine the direction whether it's right or wrong?
 
  • #40
hooman said:
the statement is wrong. the right one is the resultant force per unit length is actually acted on Y not on X. it's a mistake in typing the question.
At least that explains the "towards X" statement.
hooman said:
so how to determine the direction whether it's right or wrong?
Do you know how to find the force/length between two current-carrying wires? Start there.

Try this: Magnetic Force Between Wires
 
  • #41
Doc Al said:
At least that explains the "towards X" statement.

Do you know how to find the force/length between two current-carrying wires? Start there.

Try this: Magnetic Force Between Wires
what does it means by pointing towards X? yes, I do know how to find F/l
 
  • #42
Doc Al said:
At least that explains the "towards X" statement.

Do you know how to find the force/length between two current-carrying wires? Start there.

Try this: Magnetic Force Between Wires
but, in the question in the link that you gave, i don't know how to do it because the question itself doesn't give any value
 
  • #43
As we know a current carrying wire will induce a magnetic field around it. This field will be clockwise around the wire in the direction of current. Both wire Y and Z will exert a force on X.

By looking at the direction of the magnetic field from Y and then Z at the side of X (either into or out of the paper) you can use the hand rules (movement, flux & current) you can work out which way the wire will move.

Using the formula in the attachment you can then calculate the force and hence the direction and value of current in the question.
 
  • #44
Considering the figure as it is ,
Force on X due to Y is towards left
Force on X due to Z is towards right.
As net force on X is towards left ( see the attachment ).
F(y) > F (z).
F (net) = F(y) - F( z)
50 x 10^(-5) = 25 x 10^ (-5) - (20xI /6) x 10^(-5)
Solving we get negative value for I which is meaningless . In my opinion it should not be.
So direction of current in Z should be downward.
Then due to both Y and Z forces will be towards X.
 

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