# Magnetic Flux Density

## 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/cm2. 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 cm2.  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 cm2, what is the flux density in Gauss?

Solution:

According to Flux density formula      B = Φ/A

Then                                                    10,000 Mx/5cm2 = 2000 Mx/cm2

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 = 103 G

### The TESLA:

In SI, the unit of flux density B is webers per square meter (Wb/m2).  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 × 102 m

1 m2 = 10,000 cm2 or 104 cm2

These conversions are from the larger m and m2 to smaller units of cm and cm2. To go the opposite way.

1 cm = 0.01 m or 1 × 10-2 m

1 cm2 = 0.0001 m2 or 1 × 10-4 m2

As an example, 5 cm2 is equal to 0.0005 m2 or 5 × 10-4 m2. The calculations for the conversion are

5 cm2 × 0.0001m2/cm2 = 0.0005m2

In powers of 10, the conversion is

5cm2×  1×10-4m2/cm2 = 5×10-4m

In both cases, note that units of cm2 cancel to leave m2 for the desired units.

Example:

With the flux of 4000 μWb through an area of 0.0005m2, what is the flux density B in tesla units?

Solution:

B = Φ/A = 4000×10-6Wb/5×10-4m2

=400/5 × 10-2

= 80 × 10-2 Wb/m2

B = 0.80 T

The Tesla is a larger unit than the Gauss, as

1 T = 1 × 104 G

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

20000 G/1×104 G/T  =  2×104T/1× 104  = 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.

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