# A different answer with Ampere's Law

Consider a circular loop of radius r and a wire of finite length which lies along the axis of the loop. Current I flows through the wire and.
I am trying to to find $$\int \vec B \bullet d\vec l$$ over the circular loop.
If I find magnetic field at a point on the loop And integrate it I get a non-zero answer but when I use Ampere's Law
$$\int \vec B \bullet d\vec l =\mu I$$ here the current which pierces the loop is zero so the integral turns out to be zero.
Why does Ampere's law give a different answer?

• You are simply making the mistake that $\int B\cdot d\ell = 0 \rightarrow B=0$, which is not necessarily true – Triatticus Jul 12 '20 at 17:45
• How do you account for the current in the wire? I think if you consider charge accumulation at the ends of the wire you would end up with the desired result. – Still_a_kid Jul 12 '20 at 18:37