What is the last step in the derivation of the Biot Savart Law?

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Homework Help Overview

The discussion revolves around the derivation of the Biot-Savart Law, focusing on the final steps of the derivation process. Participants are examining the transition from the B vector to dB and questioning the cancellation of the cross product dL2.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the reasoning behind the last step of the derivation, particularly how certain terms are manipulated. Questions are raised about the definitions and relationships between the Biot-Savart Law, Ampere's Law, and the Lorentz force.

Discussion Status

The discussion is ongoing, with participants seeking clarification on terminology and the derivation process. Some guidance has been offered regarding the need to understand the laws involved, but no consensus has been reached on the specific derivation step in question.

Contextual Notes

There appears to be some confusion regarding the correct terms and laws related to the Biot-Savart Law, which may be affecting the understanding of the derivation. Participants are encouraged to clarify their knowledge of the relevant laws before proceeding.

CoolDude420
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Homework Statement


Hi,

So I'm having some trouble deriving the biot savart Law. We have been given a derivation in the notes and I understand everything up until the last step which is labelled in the picture?

2cdb94b9b9.png


Equating the two,
ff817eeb61.png


How did the B vector turn into dB? It seems like he canceled the cross product dL2 part on both sides? How is that possible?

Homework Equations

The Attempt at a Solution

 

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I think you are not having the knowledge of correct terms used in different laws. Please first make sure you know what is Biot savart law, it is about what. Also first learn what is Ampere's law and what is Lorentz force?
 
Let'sthink said:
I think you are not having the knowledge of correct terms used in different laws. Please first make sure you know what is Biot savart law, it is about what. Also first learn what is Ampere's law and what is Lorentz force?

I'm trying to derive the Biot Savart Law. Lorentz force is covered in a later chapter. I realize that what I have stated up there is not in fact Amperes Law but simply a component of the Lorentz Force.
 
First from the book you just write down the three laws you are naming. Derive them later.
 

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