Magnetic field created by a wire

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Homework Help Overview

The discussion revolves around calculating the magnetic field created by a semi-infinite wire at a point P, with the original poster noting a discrepancy in their understanding of the magnetic field's magnitude compared to the expected answer.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the difference between the magnetic field from an infinitely long wire versus a semi-infinite wire, questioning how the end effects influence the field calculation. There is discussion about whether the field should be halved due to the semi-infinite nature of the wire.

Discussion Status

Participants are actively engaging with the problem, clarifying concepts related to the magnetic field and discussing the implications of wire length on the calculations. Some guidance has been offered regarding the symmetry of the problem and the effects of wire length on the magnetic field.

Contextual Notes

The original poster has indicated that they are new to the topic, which may affect their understanding of the underlying principles. There is also mention of homework constraints that may limit the exploration of certain methods.

Eitan Levy
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Homework Statement


upload_2018-1-12_19-35-56.png

x represents the distance between the wire and P.
The wire has infinite length.
What is the magnetic field created by the wire at P?

Homework Equations


B=μ0I/2πr

The Attempt at a Solution


I thought the the first part of the wire creates a field equals to μ0I/2πx (directed inwards the paper/screen), and that the second part doesn't affect the magnetic field at P. However the answer is μ0I/4πx, where is my mistake? I know it's a simple problem but we have just started studying this, thanks in advance.
 

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Eitan Levy said:
I thought the the first part of the wire creates a field equals to μ0I/2πx (directed inwards the paper/screen),
That's the field from an infinitely long current-carrying wire. (Meaning: No end in sight.) What you need is the field from a semi-infinite wire. (There are end effects.)
 
Doc Al said:
That's the field from an infinitely long current-carrying wire. (Meaning: No end in sight.) What you need is the field from a semi-infinite wire. (There are end effects.)
So basically because it's a semi infinite wire I need to divide the field it creates by two?
 
Eitan Levy said:
So basically because it's a semi infinite wire I need to divide the field it creates by two?
Exactly. (You can appeal to symmetry. An infinitely long wire can be thought of as two semi infinite wires joined together. So each piece contributes half.)
 
You can find it by mathematics too, hope it can help you :wink:
 

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I would go with Biot-Savart. I guess that's what post 5 tries to do.
 

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