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Can I apply Ampere's law if the infinite current carrying wire is not perpendicular to the closed loop along which I calculate the line integral of magnetic field? Will that result in the component of current along the perpendicular direction to the planar loop that I have considered? If so could you provide a general proof or derivation with any general angle between the plane and current carrying wire ?

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Ampere's Circuital Law:

$$\oint \vec B\cdot d\vec l=\mu_oI_{net}$$

The value $I_{net}$ shows that net electric current flowing along normal to the plane of closed loop.

Therefore if the plane of closed loop is inclined to the infinite wire carrying an electric current $I$ at an angle say $\theta$ then $I_{net}=I\cos\theta$ will be net current in this case.

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  • $\begingroup$ Thank you for answering. Could you please provide any proof for the Ampere's law with the angle between wire and plane being any general angle theta? $\endgroup$ – Sai Krishna Garlapati May 1 '20 at 11:25
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Yes, you can. Ampère's law states that the result of the integral is independent of the path. It only depends on the amount of current enclosed by it.

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