# Magnetic Flux Density

Magnetic flux density (B) is the quantity of *magnetic flux* (Φ) per unit area (A), measured at right angles to the magnetic field. It is measured in either *tesla* (T) or *weber per square metre* (Wb/m^{2}) – the former being more commonly used.

Magnetic flux density may be calculated by using the following equation:

#### Worked Example 1

A magnet produces a flux of 180 μT through a rectangular region of width 30 mm and height 40 mm, measured at right angles to the field. Find the magnetic flux density.

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The first step is to convert all lengths to metres, so the width, W = 0.03 m and the height, H = 0.04 m. Hence the area, A = W × H = 0.0012 m^{2}. (See the Maths > Area topic for more information on calculation of areas in engineering.)

B = Φ / A

= 180 × 10^{–6} / 0.0012

= 0.15 T

#### Worked Example 2

Find the total magnetic flux produced by an electromagnet through a circular pole face of radius 50 mm, if the flux density is 1.8 T.

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The area, A = π r^{2} = π × 0.05^{2} = 0.0078539816 m^{2} (once again remembering to convert all lengths to metres before use).

The total flux, Φ = B × A

= 1.8 × 0.0078539816

= 0.014 Wb or 14 mWb (to 2 d.p.)