Current loop and the associated magnetic field under mirror reflection Let a circular current loop in the $xy$ plane carries a current in the counterclockwise sense. Therefore, it produces a magnetic field in the $+z$ direction (think of it as an arrow parallel to the $+z$-axis). Now consider reflecting this by placing a mirror in the $yz$ plane. Of course, in the image, the current will flow in the clockwise sense. But what would be the direction of the magnetic field in the mirror image?
Case I Should it remain unchanged i.e. continue to point along the $+z$-axis? If so, is it not a problem that the image does not correspond to a real physical situation (because in the real world, a clockwise current will produce a magnetic field in the $-z$-direction)? If this is really the case, this would imply that parity is violated (which is not true for electromagnetism).
Case II On the other hand, if you think that in the image the magnetic field points in the $-z$-direction, how will you explain that? Because if we think that the magnetic field is represented by an arrow (I mean, a real solid arrow made of metal or something) along $+z$, that arrow cannot be flipped by reflecting it in a mirror in the $yz$ plane. You are not allowed to use the laws of physics of the real world in the reflected world. You have to first know what you will see in the mirror and then decide whether that mirror image corresponds to the real-world situation.
 A: It is your case II.
You stumbled upon the fact that
the magnetic field $\vec{B}$ is not a vector, but a pseudovector.
That means it flips direction when going to the mirrored situation.

(image from Wikipedia - Pseudovector)
So you can't take the intuitive picture of magnetic field lines
(like being arrows made of metal) literally.
For pseudovectors this intuition leads astray.
By the way: This odd mirror behavior applies to other pseudovectors
(like angular momentum, torque, angular frequency) as well
A: Some physical quantities that most of us treat as vectors, they are indeed pseudovectors, whose nature can be appreciated when you do reflections as a transformation of coordinates.
Examples of pseudovectors are angular velocity $\omega$, force moment and torque $M$, angular momentum $\Gamma$, and the magnetic field $b$.
As a rule of the thumb, all these vectors appears in formulas relating two vectors and the pseudovectors through a vector product (or a curl operator)

*

*$v = \omega \times r$ in the rigid body rotation;

*$\Gamma = r \times Q$ for the angular momentum of a point particle;

*$M = r \times F$ for the force moment of a point particle;

*$F = q v \times b$ for Lorenz force in absence of electric field;

where position $r$, velocity $v$, force $F$, linear momentum $Q$ are vectors.
