Magnetic Flux Density Direction

[DiamondV]

Would the direction of the Magnetic Flux Density vector B at the south side be towards the south pole like this?

and is the direction for B correct for the other side?

One more thing, how can magnetic flux density be a vector and have a direction when its sort of a density, I mean its over an area, how can you make that a single vector? Its sort of like a property.

 

[Chandra Prayaga]

1. I don't see the difference between the two figures, except that you drew two extra arrows. Both figures are correct. The field is toward the south pole, and out of the north pole.
2. Don't read too much into the name. The same "flux density" is also called the magnetic field B. The magnetic flux through an area is defined as the magnetic field multiplied by the area (actually a dot product between B and the area vector A). So if you want to call magnetic field as the magnetic flux divided by the area, and thus call it the magnetic flux density, so be it. It is still the magnetic field, and is an honest to goodness vector.