Magnetic Flux Density
Flux density is the measure of the number of magnetic lines of force per unit of cross-sectional area.
While the total amount of the flux produced by a magnet is important, we are more interested in how dense or concentrated, the flux is per unit of cross-sectional area. Flux per unit of cross-sectional area is called flux density.
Magnetic Flux Density Formula
Its letter symbol is B. The relationship between total flux and flux density is given by the following equation:
$B=\frac{\varphi }{A}$
Where
B=flux density in Tesla
φ=total magnetic flux in weber
A= Cross-sectional area in square meter
Magnetic Flux Density Unit
The SI Unit for flux density is the Tesla (T) which is defined as;
$B=\frac{\varphi }{A}$
$B=\frac{Wb}{{{m}^{2}}}=Tesla$
“If one line of magnetic field passes normally through m2 area, the magnetic flux density, B, will be one Tesla,
Example of Magnetic Flux Density
Calculate the flux density in a ferromagnetic material with a cross-sectional area of 0.01 m2 containing 100 lines.
Solution
We know that 100 lines equal to 1 μWb. By using following formula, we can calculate the flux density B
$B=\frac{\varphi }{A}$
$B=\frac{1~\mu ~Wb}{1*{{10}^{-2}}{{m}^{2}}}=\frac{1*{{10}^{-6}}~Wb}{1*{{10}^{-2}}{{m}^{2}}}=1*~{{10}^{-4}}~T$
Example of Magnetic Flux Density
Determine the cross- sectional area of a toroid that has a flux of 0.5 Wb and a flux density of 25 T.
Solution
We have the following formula to calculate cross-sectional area:
$A=\frac{\varphi }{B}=\frac{0.5~Wb}{25~{}^{Wb}/{}_{{{m}^{2}}}}=2*~{{10}^{-2~}}{{m}^{2}}$
Example of Magnetic Flux Density
An air core coil has 0.65 μ Wb of flux in its core. Calculate the flux density if the core diameter is 4 cm.
Solution
First calculate the area of the core:
$A=\pi ~{{r}^{2}}=3.14*{{\left( 0.02m \right)}^{2}}=1.256*~{{10}^{-3}}~{{m}^{2}}$
Now, calculate the flux density using following formula:
$B=\frac{\varphi }{A}=~\frac{0.65*~{{10}^{-6}}~Wb}{1.256*~{{10}^{-3}}~{{m}^{2}}}=5.175*~{{10}^{-4}}~T$
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