Right hand thumb rule and magnetic flux/density

[DiamondV]

Homework Statement

We were given two diagrams in our notes about the right hand thumb rule.

Homework Equations

The Attempt at a Solution

Is the second image(one on the right) wrong? Isnt the magnetic flux density supposed to be clockwise in second image?
Also is this statement correct: Magnetic flux density is the amount of magnetic flux lines passing through an area.?

 

[Geofleur]

The picture on the right is correct and, viewed from the top down, the magnetic lines are directed clockwise. Pay close attention to where the lines go behind the wire versus in front.

Regarding the second question, usually that's just called the magnetic flux, though I think some authors may refer to the same thing as the magnetic flux density. Also, "the number of field lines passing through an area" is an integer, while the actual flux can be any real number. The description in terms of number of lines passing through is really just a way to understand conceptually how the flux behaves - the larger the number of lines passing through a given area, the stronger the flux. We can say that the actual magnetic flux is proportional to the number of field lines passing through an area.

EDIT: I did a little searching and found that the magnetic flux density is defined as the magnetic flux divided by the area being considered.

 

[Geofleur]

It's the field lines that are directed clockwise in the right figure, not the flux or the flux density. The magnetic field is a vector, whereas the magnetic flux and flux densities are just numbers!