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# Magnetic Flux Density | Definition and Formula

## 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:

$B=\frac{\varphi }{A}=~\frac{0.65*~{{10}^{-6}}~Wb}{1.256*~{{10}^{-3}}~{{m}^{2}}}=5.175*~{{10}^{-4}}~T$

Mr. Ahmed Faizan Sheikh, M.Sc. (USA), Research Fellow (USA), a member of IEEE & CIGRE, is a Fulbright Alumnus and earned his Master’s Degree in Electrical and Power Engineering from Kansas State University, USA.

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