# Magnetic Flux Density

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#### What is Magnetic Flux Density?

The magnetic flux density or magnetic field strength is the number of magnetic lines of force passing through a unit area of material.
It is denoted by the capital letter B, and is measured in tesla.
Its magnitude is determined by the following equation:
$$\bbox[10px,border:1px solid grey]{B = {\Phi \over A}} \tag{1}$$
where $\Phi$ is the number of flux lines passing through the area A.
By definition, $$1 \,T = 1 \, Wb/m^2$$
Fig. 1: Magnetic Flux Strength and Density.
Example 1: For the core of Fig. 2, determine the flux density $B$ in teslas.
Fig. 2: For Example 1.
Solution: $$B=\frac{\Phi}{A}=\frac{6 \times 10^{-5} \mathrm{~Wb}}{1.2 \times 10^{-3} \mathrm{~m}^{2}}=5 \times 10^{-2} \mathbf{T}$$
Example 2: In Fig. 2, if the flux density is $1.2 \mathrm{~T}$ and the area is $0.25 \mathrm{in.}^{2}$, determine the flux through the core.
Solution: By Eq. (1),
$$\Phi=B A$$
However, converting $0.25 in. ^{2}$ to metric units,
\require{cancel} \begin{aligned}A=0.25 \cancel{in.}^{2}( & \left.\frac{1 \mathrm{~m}}{39.37 \cancel{ in. }}\right)\left(\frac{1 \mathrm{~m}}{39.37 \cancel{in. }}\right)=1.613 \times 10^{-4} \mathrm{~m}^{2} \\\Phi & =(1.2 \mathrm{~T})\left(1.613 \times 10^{-4} \mathrm{~m}^{2}\right) \\& =\mathbf{1 . 9 3 6} \times \mathbf{1 0} 0^{-4} \mathbf{W b}\end{aligned}

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