The size and direction of magnetic induction and force

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Homework Help Overview

The problem involves four long straight parallel wires carrying electric current in a vacuum, with a focus on determining the size and direction of magnetic induction and the force acting on one of the wires. The context is rooted in electromagnetism, particularly concerning magnetic fields and forces due to current-carrying conductors.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to compute the resulting magnetic induction and the force on the wire using Ampere's right hand rule and is seeking guidance on these calculations. Some participants question the terminology used, specifically whether the problem is asking for magnetic induction or magnetic field strength, suggesting that the steady-state nature of the system may imply certain conditions about the magnetic induction being zero.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. There is a mix of guidance offered regarding the use of the Biot-Savart law and the Lorentz force, but no consensus has been reached on the correct approach or terminology.

Contextual Notes

Participants are discussing the implications of the steady-state condition of the system and how it affects the calculations related to magnetic induction and force. There is also a request for hints rather than complete solutions, in line with homework help guidelines.

darkprior
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Homework Statement


Hello, I have this problem:
Four long straight parallel wires are placed in vacuum according to the picture, the distance between each wire is a = 20 cm. Through each wire flows electric current I = 20 A in the specified direction. What is the size and direction of magnetic induction in the middle of this system? What is the size and direction of the force acting on one meter of the bottom left wire?

Homework Equations


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The Attempt at a Solution


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I drew the line of forces following the Ampere's right hand law, and also the vectors of magnetic inducion of each wire:

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now my answer is how do I compute the size of the resulting induction, and my second question is how do I find out the force acting on 1 meter of the lower left wire?

Thanks in advance for advices
 
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Do they really want to know the strength of magnetic induction? Won't that be zero, because induction arises from the time variation of mag fields and this system is steady state? The vectors you have drawn are of mag fields ##\vec B##, not of induction.

If it's just the mag field that's wanted, not induction, then the Biot-Savart law will do the job.
 
andrewkirk said:
Do they really want to know the strength of magnetic induction? Won't that be zero, because induction arises from the time variation of mag fields and this system is steady state? The vectors you have drawn are of mag fields ##\vec B##, not of induction.

If it's just the mag field that's wanted, not induction, then the Biot-Savart law will do the job.

Yes they want the strength of magnetic induction, if it is zero, then fine I will write it as a solution. Now can you please give me a hint with identifying the direction and strength of the force acting on one meter of left bottom wire, please?
 
darkprior said:
can you please give me a hint with identifying the direction and strength of the force acting on one meter of left bottom wire, please?
It is the Lorentz Force, which is explained here.
 
andrewkirk said:
It is the Lorentz Force, which is explained here.

Thank you for your help and time
 

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