# Magnetic flux + density

## Main Question or Discussion Point

I read somewhere that increasing the current flowing through a solenoid will increase the magnetic flux density but cannot increase the magnetic flux.

From what I gather magnetic flux is the space the magnetic field covers or the range of the magnetic flux lines and flux density is how many flux lines there are within the range of the magnetic field.

If I had a regular permanent magnet and a more powerful rare earth magnet which was exactly the same size as the regular magnet obviously the earth magnet would have a greater flux density but would it have a greater magnetic flux? Would its magnetic flux lines reach greater distances than the regular magnet?

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marcusl
Gold Member
I read somewhere that increasing the current flowing through a solenoid will increase the magnetic flux density but cannot increase the magnetic flux.
Since flux requires a definition of the surface being considered (see below), this is not a complete statement. One example of a more complete statement: the total magnetic flux crossing a plane perpendicular to the solenoid axis and located at the solenoid midpoint is zero. For this geometry the statement is true. It may not hold for other cases.

From what I gather magnetic flux is the space the magnetic field covers or the range of the magnetic flux lines and flux density is how many flux lines there are within the range of the magnetic field.
Not exactly. Magnetic flux density is the number of flux lines, or lines of magnetic force, per unit area. It is denoted by the symbol B, and is also called the magnetic induction, or sometimes, confusingly, magnetic field. Flux, on the other hand, is the total number of lines crossing a given surface, so it is a surface integral of B.

If I had a regular permanent magnet and a more powerful rare earth magnet which was exactly the same size as the regular magnet obviously the earth magnet would have a greater flux density but would it have a greater magnetic flux?
I hope this is clearer from the discussion above.
Would its magnetic flux lines reach greater distances than the regular magnet?
Theoretically, the field lines can fill all of space, but with vanishing density so the magnetic induction B approaches zero far away. The stronger magnet will produce a stronger induction at the same distance, or the same induction at a greater distance.