Hi. I am trying to figure this out. I figure it'd be best to do with an example. Say we have a bar magnet, N and S poles. Surrounded by vacuum with μ=μ0. CASE 1: Then. We put a high permeability material μr x just to the left of the magnet say. Now, from what I have been taught I understand that most of the flux will go through that since the flux will try to follow the path of least resistance. CASE 2: But now, I put another identical high permeability substance x to the right. With the same idea, the flux would try to go through this too. But since flux is limited (is it?), it will divide and half will go through the left and the other half through the right. So far so good? Ok. Now the part I don't understand is the equations don't add up the way I am doing it. If we do B=μH for CASE 1, say we get B=a. OK. But now if we do B=μH for CASE 2, we have 2 paths for the flux and ==> (B=μH=a) + (B=μH=a)=2a. Surely the flux density can't just double because I put another piece of metal around it. What I'm trying to get at is basically this, how does the equation B=μH "know" about the area outside the one it is measuring? How will it know if it is filled with very high permeability substance or just vacuum? A theory I have is that H will decrease accordingly as we increase the μ around said magnet. Don't know if it is right or wrong. Another doubt I have is. If H doesn't depend on μ, then is it always uniform and always present around a bar magnet irrelevant of its surroundings? (This doesn't sound right?). Is it like a theoretical field whereas B is the actual field in real life? What am I missing?