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

[CoolDude420]

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?

Equating the two,

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

 

[Let'sthink]

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?

 

[CoolDude420]

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.

 

[Let'sthink]

First from the book you just write down the three laws you are naming. Derive them later.