Deriving Biot Savart's law from Ampere's law

[McLaren Rulez]

Can anyone help me with this? My textbook (Young and Freedman's University Physics) says that Ampere's law can be extrapolated to give Biot Savart's law but I'm not sure how to go about it.

 

[johnsmi]

Here is a proof I found because i am too lazy to deal with maths.
Anyway, it is pritty clear they are connected since both deal with the relation beteen I and B

http://www.abbasem.net/articles/axiomatic.pdf

Thumbs up and good luck

 

[Meir Achuz]

I have not looked at that paper in detail, but it does not claim to derive B-S from Ampere.
What I have read on that website is all wrong. I showed the mistake to the author of the website, but he did not send me the $5,000.

You have to be more specific, "Ampere's law" can refer to two different laws,
"Biot=Savart's law" can be in differential or integral form.

 

[gabbagabbahey]

I think you can derive the Biot-Savart Law in the form

$$\textbf{B}(\textbf{x})=\frac{\mu_0}{4\pi}\int\frac{\textbf{J}(\textbf{x}')\times (\textbf{x}-\textbf{x}')}{|\textbf{x}-\textbf{x}'|^3}d^3x'$$

From Ampere's law (for magnetostatics) in the form $\mathbf{\nabla}\times\textbf{B}=\mu_0\textbf{J}$ and $\mathbf{\nabla}\cdot\textbf{B}=0$, along with the boundary condition that the field goes to zero at infinity (falls of sufficiently quickly far from the source currents). If that's what you are interested in, I'd start by taking the curl of both sides of Ampere's Law, and then solve the resulting vector form of Poisson's equation for each Cartesian component of $\textbf{B}$ via Fourier Transform methods.

 

[McLaren Rulez]

Okay I know Ampere's law and Biot Savart's law in their most basic forms so I don't understand the explanation in the previous post. I'm a college freshman so I only know the integral form of Ampere's law also. So how can I derive Biot Savart's law from Ampere's law.