Ampere's law for a loop with zero enclosed current

Question

Imagine a wire with current I flowing through it. If we take a closed loop that doesnt contain the I the line integral will be zero. Does this means magnetic field is zero ? Also does Ampere law calculating the total magnetic field or only the sum of magnetic fields from the currents that are enclosed in the loop?

Answer 1

of course not. Unless you can argue that the magnetic field is constant over the loop so that $\oint \vec B\cdot d\vec \ell= \vert\vec B \vert \oint d\ell$ you cannot deduce anything about $\vec B$.

In the same way if a Gaussian surface encloses no charge it does not mean the field is 0 unless the magnitude of $\vec E$ is constant over the surface.