## What is Flux Density?

As shown in figure (a), the flux density is the number of magnetic fields lines per unit area of a section perpendicular to the direction of flux. Flux Density symbol is ** B**, as a formula

*B = Φ/A*

Where ** Φ **is the flux through an aria

*A*, and the flux density is

*B*

## Flux Density Units:

### The GAUSS:

In the cgs system, this unit is one line per square centimeter, or 1 Mx/cm^{2}. As an example in figure (a), the total flux ** Φ** is 6 lines, or 6 Mx. At point P in this field, however, the flux density B is 2 G because there are 2 lines per cm

^{2}. The flux density has a higher value close to the poles, where the flux lines are more crowded.

As an example of flux density, B for a 1 lb magnet would be 1000 G at the poles. This unit is named for Karl F. Gauss (1777-1855), a German mathematician.

### Example:

With a flux density of 10,000 Mx through a perpendicular area of 5 cm^{2}, what is the flux density in Gauss?

**Solution:**

*According to Flux density formula B = Φ/A*

*Then 10,000 Mx/5cm ^{2} = 2000 Mx/cm^{2}*

* B = 2000 G*

As a Typical value, B for the earth’s magnetic field can be about 0.2 G: a large laboratory magnet produces B of 50,000 G. Since the Gauss is so small, it is often used in kilogauss units, where 1 KG = 10^{3} G

### The TESLA:

In SI, the unit of flux density B is webers per square meter (Wb/m^{2}). One Weber per square meter Is called a ** Tesla, **abbreviated T. This unit is named for Nikola Tesla (1857-1943), a Yugoslav-born American inventor in electricity and magnetism.

### When converting between cgs and mks units note that

1 m = 100 cm or 1 × 10^{2} m

1 m^{2} = 10,000 cm^{2} or 104 cm^{2}

These conversions are from the larger m and m^{2} to smaller units of cm and cm^{2}. To go the opposite way.

1 cm = 0.01 m or 1 × 10-2 m

1 cm_{2} = 0.0001 m^{2} or 1 × 10^{-4} m^{2}

As an example, 5 cm^{2} is equal to 0.0005 m^{2} or 5 × 10^{-4} m^{2}. The calculations for the conversion are

5 cm^{2} × 0.0001m^{2}/cm^{2 =} 0.0005m^{2}

^{ }

^{ }

In powers of 10, the conversion is

5cm^{2}× 1×10-4m^{2}/cm^{2} = 5×10^{-4}m^{2 }

In both cases, note that units of cm^{2} cancel to leave m^{2} for the desired units.

Example:

With the flux of 4000 μWb through an area of 0.0005m^{2}, what is the flux density B in tesla units?

^{ }

*Solution:*

*B = Φ/A = 4000×10 ^{-6}Wb/5×10^{-4}m^{2}*

^{ } =400/5 × 10^{-2}

^{ } = 80 × 10^{-2} Wb/m^{2}

^{ }B = 0.80 T

* *

* *

The Tesla is a larger unit than the Gauss, as

1 T = 1 × 10^{4} G* *

^{ }

^{ }For example , the flux density of 20,000 G is equal to 2 T. the calculations for this conversion are

20000 G/1×10^{4} G/T = 2×10^{4}T/1× 10^{4} = 2T

Note that the G units cancel to leave T units for the desired answer. Also, the 1/T in the denominator becomes inverted to T units in the numerator.