Magnetic Units and Measurements AN0045

APPLICATION NOTE AN0045/2

Magnetic Units and Measurements

1. Measurement Units Then B = 4p x 10-7 x 80 ≈ 1 x 10-4 T

Magnetic flux density = B Tesla is the preferred unit for flux density in the SI system. A magnetic field sensor can only be said to Magnetic field strength = H measure flux density.

SI (Système Internationale) is the preferred system of measurement for Bartington Instruments. However, 2. Conversion Table measurements are still frequently expressed in The most common conversion performed will be units based on the CGS (centimetre–gram–second) from Tesla to Gauss, and vice-versa. The following system. For clarity the following relationships may table may be helpful. be useful. SI units are shown below with their CGS numerical (but not dimensional) equivalents.

SI CGS Measurement SI CGS 1 Tesla 10 kGauss -2 4 B 1 Wbm 10 G 1 mT 10 G (Weber per (Gauss) metre2) 1 mT 10 mG or 1 T 1 nT 10 mG (Tesla) H 1 Am-1 4π x 10-3 Oe CGS SI (Amperes (Oersted) 1 kGauss 100 mTesla per metre) 1 G 100 mT

1 mG 100 nT The fundamental equation describing the 1 mG 100 pT relationship between H, B and the permeability of Table 1. Conversion of SI and CGS Unit free space m0 is:

B = m H 0 3. Vector Measurements with 3 Axis Sensors It will be seen that the term 4p occurs in the CGS units shown above. The SI units, however, are Each axis produces an analogue output Va in rationalised indirectly by incorporating this term in response to flux density B in the relationship: m0. Thus in the SI system: Va = B cos q -7 -1 m0 = 4p x 10 Hm (Henries per metre). where q is the angle between the flux direction and Example: for free space: the direction of the individual sensing element. If H = 80 Am-1

www.bartington.com APPLICATION NOTE AN0045/2

The scalar value of a magnetic field may be computed from the individual X, Y and Z vector components, using the RSS (Root of Sum of the Squares) where:

B = (Vx2 + Vy2 + Vz2)½

Note: There will be a small error in the result of the calculation of the total field, due to the small error in the orthogonality between the sensing elements. This will be particularly noticeable when the total field is computed from the values measured with several orientations of the sensor. The sensor is extremely sensitive in the measurement of small variations in the total field, provided that the orientation is constant, i.e. the detector is stationary. The sensor is therefore limited in applications requiring total field measurement while moving, as in a towed ferrous metal detector, by the orthogonality error within the specified tolerance.