Ampere’s law problem

1. The problem statement, all variables and given/known data
A conductor carrying current ##I## is in the form of a semicircle AB of radius ##R## and lying in xy-plane with it’s centre at origin as shown in the figure. Find the magnitude of ##\oint \vec{B}\cdot \vec{dl}## for the circle ##3x^2+3z^2=R^2## in the xz plane due to curve AB.

(Ans: ##(2-\sqrt{3})\frac{\mu_0 I}{2}##)

2. Relevant equations

3. The attempt at a solution
From Ampere’s law:
$$\oint \vec{B}\cdot \vec{dl}=\mu_0 I_{enclosed}$$
There is no current passing through the loop ##3x^2+3z^2=R^2##, so for this loop, RHS for ampere’s law is zero hence answer should be zero but it isn’t. :confused:

Any help is appreciated. Thanks!

Attached Images
File Type: png bdl.png (4.3 KB)

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