The idea that magnetic fields surround current-carrying objects was unheard of in the 1820’s. Ampere in his time conceptualized the magnetic fields around wires as “corkscrew-like” molecular currents expressed with vectors and integrals.
Michael Faraday, an English physicist who continued Ampere’s experiments after his death in 1836, would be the first to visualize these magnetic fields. Utilizing iron filaments, a ferromagnetic material that becomes strongly magnetized when placed in a magnetic field, his “lines of force” matched Ampere’s predictions!
Magnetic field around a wire 
Magnetic field around a solenoid. 
We, nearly two hundred years later, can perform our own iteration of this experiment through a COMSOL simulation that upholds Ampere’s and Faraday’s experiments. In each case, the magnetic field is created by a current flowing through each geometry is visualized:
Magnetic field around a wire: 
Magnetic field around a solenoid: 