Hi, I have explained with an interesting 3D Model and 3D ANIMATION, the basic concept and equation derivation for Magnetic Field Strength 'B' around a wire when an electric current is passed through it :
Case 1: a FINITE straight wire
Case 2: an INFINITELY LONG Straight wire
I have shown a DC current experimental arrangement using a Battery source, for simplicity. If in case an AC current source is used, the current direction will reverse every time as per the frequency of current like 50Hz/60Hz. Then the Magnetic Field DIRECTION will also reverse with the exact same frequency. Note that the Strength of the magnetic field will remain same at any instant as per the equation shown.
This concept of Magnetism created by Electricity was a fundamental discovery of physics. The other concept of Electro-Magnetism showed that the Electricity is also be created by Magnetism.
Have a great day
kaustubhan