In my class, I was taught about Biot Savart Law and how to calculate direction of magnetic field as a cross product of radial vector from current element and the length vector of current element.
But I am not able to understand why magnetic field have been assigned such a direction, how did Biot and Savart know that it is perpendicular to both the current element vector and the position vector of the point where field is to be determined?
We define the direction of electric field as the force acting on a positive test charge. Is there some definition like that with magnetic field too?
Do vector fields have an 'inbuilt' direction of their own or its just by convention?
If vector fields really have some inbuilt direction, how did Biot and Savart determined that of magnetic field?