Magnetic forces on current-carrying wires

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Homework Help Overview

The discussion revolves around the magnetic forces acting on a current-carrying wire, specifically wire X, influenced by two other wires, Y and Z. Participants are exploring the relationships between the forces exerted by these wires and the resultant magnetic force on wire X.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to clarify the direction and magnitude of the forces acting on wire X, questioning the meaning of terms like "pointing towards X." There is discussion about using the right-hand rule to determine force directions and whether to consider these directions as positive or negative in calculations.

Discussion Status

There is ongoing exploration of the forces acting on wire X, with participants raising questions about the contributions from wires Y and Z. Some have provided interpretations of the problem's wording, while others are seeking clarity on how to approach the calculations based on the given information.

Contextual Notes

Participants note confusion regarding the phrasing of the problem, particularly the direction of the resultant force on wire X. There is also mention of the assignment context, which may impose specific constraints on how the problem should be interpreted.

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..
 

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