hi kira506!
the biot savart law includes a
cross product …
are you not familiar with cross products?
the magnetic field lines for a straight current-carrying wire will always be circles round the wire, whether it's finite or infinite (this is obvious, from symmetry)
but the circles will all be the same size for an infinite wire
in other words, the magnetic field strength will be a function B(r) that
only depends on the distance r from the wire
however, for a
finite wire, B will be a function of z as well (the distance along the wire): B(r,z)
when it's just B(r), you can easily tell what the function B is
when it's B(r,z), you can't, and you need to use the biot-savart law to calculate it in detail
have you watched the video i referred to?
is there any part of it you don't understand?