# Why is the unit of Magnetic flux is $T m^2$ and not $T m^{-2}$

If Magnetic flux is the strength of magnetic field that passes an unit area, (thereby flux PER unit area),then why is it given in units of $$T m^2$$ and not $$T m^{-2}$$?

• Because T (Tesla) is not the unit of magnetic field $\mathbf{H}$ but the unit of magnetic flux density $\mathbf{B}$. Sep 12 '20 at 13:53
• Tesla is unit of density so to get a fluid integral on an area you need to multiply density(T) with area(m2) Sep 12 '20 at 14:44
• @Aaratrick if I go by what you said, then the definition of flux does make perfect sense. but then, what is the unit of magnetic field? also, what is this H thing? I was taught that B represents magnetic field, but you say that instead, B represents the density of the field.. Was I taught wrong? Plz clarify. Sep 12 '20 at 14:50
• You are confused between B and H. In your other question you say magnetic field has units of A/m, which is true for H-field. The two fields are not the same, though both are often referred to as the magnetic field, and they have different SI units. Sep 12 '20 at 16:20
• @isaac_samuel You can take a look here, en.wikipedia.org/wiki/Magnetic_field . As Rob Jeffries has answered, flux is defined as the product of the flux density $\mathbf{B}$ times the area. However, the magnetic field, in SI at least, is $\mathbf{H}$ and the relation between them is, $\mathbf{B}=\mu_0 \mathbf{H}$ in vacuum. As for whether you were taught correctly, I believe the distinction between the two is not done in high-school physics. Look at the Wikipedia page, I think you will understand anything you were not taught Sep 14 '20 at 14:30

The "magnetic flux density" (often called the magnetic field and given the symbol $${\bf B}$$) has SI units of Teslas, T. It is a flux density, because a Tesla is also a Weber/m$$^2$$, where a Weber, Wb, is a unit of magnetic flux.
To get a magnetic flux from a magnetic flux density, you have to integrate over an area, i.e. $$\Phi = \int {\bf B}\cdot d{\bf A}\ .$$
Clearly then, the units of flux $$\Phi$$ are either Tm$$^2$$, or Wb.