# Why is Biot–Savart law and Ampère's law different in my scenario?

If I consider a finite length of wire in which current I is flowing. if I consider a circular loop above the finite wire, such that the current passing through that circular loop is zero. According to ampere's law. The current passing through that loop is zero and hence the magnetic field in that region of loop must be zero according to ampere law But by using biot savart law , the magnetic field in that region of loop is not zero

I am confused that by using ampere's law I get that the magnetic field is zero at that region but by using biot savart law I get magnetic field is not equal to zero.

I am explaining my situation through the diagram above

• Maxwell's equations without current conservation are not internally consistent, so you can't have finite lengths of wire. You need complete circuits. Commented Jun 21 at 15:47
• My answer here touches on why this happens. Briefly, the field derived from the Biot-Savart Law vanishes If and only if there are no "sources" or "sinks" of current. Commented Jun 21 at 18:01