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If we have a current carrying loop with center at a point o, and i have a point P in this plane where im supposed to calculate magnetic field, if i consider an amperian loop with center at o and passing through P, by symmetry at all points on this amperian loop, the magnetic field should be same and since current enclosed is zero(no current cuts the amperian surface), shouldnt the magnetic field be zero?

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  • $\begingroup$ This might depend on whether you look at the field along the loop trajectory, or perpendicular to it. Check the definitions... $\endgroup$ Commented Mar 25 at 9:57

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So your argumentation using Amperes law and rotational symmetry does hold. But as mentioned in the comments you need to take care of the direction you are looking at. Your argumentation tells you, that the magnetic field threw your loop in direction of the loop, if place properly, will be zero at all points of the loop. But that does not mean, the overall magnetic field is zero there, it just means that any nonzero component has to have a direction perpendicular to the loop and therefore not contribute to the integral in Amperes law. Which might be seen relatively easily, if one imagines the kind of dipolish B-field created by your current loop.

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