Hey everyone, I was hoping you could help me solve a little problem. I'm having a little difficulty understanding why the right hand rule works for determining the direction of the magnetic field. I've found a similiar question posted here: https://www.physicsforums.com/threads/why-does-the-right-hand-rule-works.472162/ And I feel that while the answers were insightful, they kind of missed the point of the question, so I'll try to state mine in a way that can be answered in a yes -or-no manner. Suppose I have an infinately long conductive wire, and I want to determine the magnetic field around it using only maxwell's equations. Suppose I already deduced the strength of the field, and the fact that it is perpendicular to the direction of both the current and the distance from the wire (I know it is possible to do because I have done it). My question is this: can I deduce, only from maxwell's equations, whether the field will be directed into the plane of the paper or out from it? Or do I have to experimentally place a test charge close to the wire and measure the Lorentz force on it? In short, is the right hand rule a property of the magnetic field stemming directly from the mathematical description of it, or is it a purely empirical property?