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 $\mathbf{M}$.