Magnetism, what is "B"?

Question

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

Answer 1

Do you understand flux and surface density? See Magnetic Flux

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.

Answer 2

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 $\mathbf{M}$.