Amperes circuital law for finite length of wire

[jd12345]

Why is that amperes circuital law gives the same magnetic field around a finite legnth of wrie as if it is an infintie legnth of wire?
By biot-savarts law we know that for a finite length of wire magnetic field is
μ i ( cos θ1 - cos θ2)/ 2∏r

I searched this question in google and one of the answer was that magnetic field will not be tangential to the circular loop we imagine around the wire. So when we integrate magnetic field cannot be calculated

But that's wrong isn't it? By biot-savarts law we see that magnetic field is tangential around the wire along the circular loop with the constatn value as given above. So we can integrate it and find the magnetic field using amperes law
But answer does not come. Why?

Sorry if it ahs been asked again. Give me the link if it has been. Thank you!

 

[Simon Bridge]

OK - here's the link.
https://www.physicsforums.com/showthread.php?t=166197
... also see the link in that thread.

I searched this question in google and one of the answer was

... best to provide the link to the references you use.

But answer does not come. Why?

... have you tried to do the calculation?

 

[jd12345]

Yeah in your link - the reason because amperes circuital law doesn't work is as in the integral B.dl B is not constant so we cannot take out B out of the integral and find its value.
This isn't correct! Clearly B is constant around a finite length of wire having its value as
μ i ( cos θ1 - cos θ2)/ 2∏r

 

[Simon Bridge]

OK - so do it then.

 

[Meir Achuz]

Ampere's law is derived in magnetostatics from curl H =j (omitting constants),
which is derived from the B-S law by requiring div j=0 everywhere. You can see this by taking div of curl H=j. Div j does not equal zero for a finite wire, so Ampere's law does not apply. Ampere's law applies only for a closed circuit. For an infinite wire, the circuit can by closed by a semicircle of radius R which gives no contribution as R-->infinity.