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

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SUMMARY

The discussion focuses on the derivation of the Biot-Savart Law, specifically addressing confusion regarding the transition from the magnetic field vector B to the differential magnetic field dB. Participants emphasize the importance of understanding related concepts such as Ampere's Law and the Lorentz Force to grasp the derivation fully. The conversation highlights the necessity of correctly applying terms and laws in electromagnetism to avoid misunderstandings during derivation processes.

PREREQUISITES
  • Understanding of Biot-Savart Law
  • Familiarity with Ampere's Law
  • Knowledge of Lorentz Force
  • Basic principles of electromagnetism
NEXT STEPS
  • Study the derivation of the Biot-Savart Law in detail
  • Learn the mathematical formulation of Ampere's Law
  • Explore the applications of the Lorentz Force in electromagnetic theory
  • Review vector calculus as it applies to electromagnetism
USEFUL FOR

Students of physics, particularly those studying electromagnetism, educators teaching these concepts, and anyone seeking to deepen their understanding of magnetic field derivations.

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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