Figure shows an amperian path ABCDA . Part ABC is in vertical plane PSTU while part CDA is in horizontal plane PQRS . Direction of circulation along the path is shown by an arrow near point B and at D

Question

Figure shows an amperian path ABCDA . Part ABC is in vertical plane PSTU while part CDA is in horizontal plane PQRS . Direction of circulation along the path is shown by an arrow near point B and at D . ∮ B → . d l → for this path according to Ampere's law will be

TestHub · Accepted Answer

If the loop current is coming out it should be taken as positive and if it is going in it is taken as negative.
$i_{3}$ is coming out and again going in so its net contribution will be zero.
According to Ampere's law,
$\oint \vec{B} \cdot \vec{d l} = μ_{0} (Σ i_{i n s i d e})$
$= μ_{0} (i_{1} + i_{2} + i_{3} - i_{3})$
$= μ_{0} (i_{1} + i_{2})$

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