# Magnetism, what is “B”? [duplicate]

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The term "B" denotes both magnetic flux density and magnetic induction. Are the terms same? If, not what do they mean

## marked as duplicate by John Rennie, fffred, Jon Custer, AccidentalFourierTransform, rob♦Jan 25 '17 at 1:58

• You need to give us a bit more context. $\mathbf B$ is normally taken to the be the magnetic field strength i.e. the magnetic flux is $\Phi = \int \mathbf B.d\mathbf A$ and the induced voltage is then $-d\Phi/dt$. Can you explain what you mean by B denotes the magnetic induction? – John Rennie Jan 24 '17 at 16:10

What you refer to as "Magnetic flux density", would be the magnitude of the magnetic field $\mathbf B$. Magnetic flux $\Phi$ is a scalar, it is modeled as the amount of field lines passing trough a given surface thus, since it is a dot product, flux is the magnitude of the perpendicular component of the magnetic field times the surface area, $$\Phi = \int B \circ \hat n \mathcal dA = B_\perp A$$ Surface density is a quantity per unit area hence, dividing flux by area leaves you with the magnitude of the magnetic field perpendicular to the surface, $$\frac \Phi A = B_\perp$$ Finally, magnetic induction is the result of a change in flux, $$\frac {\Delta \Phi} {\Delta t} = \frac{\Delta (B_\perp A)}{\Delta t}$$ See Faraday's Law.
I think your confusion comes from an older usage of the terms $\mathbf{B}$ and $\mathbf{H}$. Old text books called $\mathbf{H}$ the magnetic field and came up with different names for $\mathbf{B}$, such as magnetic induction or magnetic flux density and etc.
Nowadays, we just call $\mathbf{B}$ the "magnetic field" and $\mathbf{H}$ is just called the "$\mathbf{H}$ field".
The difference is that $\mathbf{B}$ is due to all currents, whereas $\mathbf{H}$ is due to "free current" and the magnetization $\mathbf{M}$.