What is the basic reason behind magnetic effect of current?
The reason is special relativity. Imagine you have two charged wires with some charge density. They exert an electrostatic force on one another. Now imagine you are traveling at relativistic speed along the direction of the wires. The length contraction changes the charge density, which changes the electrostatic force between the wires. The only way to reconcile this is the existence of a magnetic force between moving charges. So different observers see the same force. They may disagree on whether it’s magnetic or electrostatic, but they agree on the end result. You should learn this in your second E&M class as an undergraduate majoring in physics or EE or something like that. You can find it in a textbook like Griffith’s E&M. This same thing happens with gravity, which has a “magnetic” analog as well which you’ll learn if you ever take a course in general relativity.
