I asked this question to several people.
Some say it is found by placing the compass around a current carrying wire. Some say magnets always exist as dipoles so field lines emerge from the north pole and end in the south pole and so it looks circular. And this user on Stack Exchange says:
Rather than constantly transforming back and forth between frames, we invent the magnetic field as a mathematical device that accomplishes the same thing.
And another user:
This electric field in the moving frame clearly exerts a radial force on any test charge originally at rest with respect to the wire in the stationary frame. But, given that there is no radial force or acceleration in the stationary frame, there also cannot be a net radial force on the charge when it is in the moving frame either. The force that counteracts the radial electric field in the moving frame is the Lorentz force due to a mystery (B-)field. As the Lorentz force due to the mysterious (B-)field ....
and I can't understand either.
If I place a proton just as in the diagram:
then from the proton's frame of reference, the protons on the wire appear to be denser than the electrons in the wire, so it must experience an outward force. So its path should be like a parabola. Field lines are found by tracing the path followed by a test charge or test mass or whatever, placing them in a field. So in case of magnetic field lines it should be a weird field line, not circular.
So why are the magnetic field lines circular? Or how is the magnetic field used as a mathematical device as mentioned?
I'm searching for an answer for three months. I got frustrated lot of times and still I am searching. Please help me. Please don't involve too much mathematics (I am just in 12th grade).