Search coil magnetometer

Principle

The inductive sensor is based on Faraday's law of induction. The temporal variation of the magnetic flux \Phi through a N turns circuit will induce a voltage e which follows : e = - N\frac{\mathrm d \Phi}{\mathrm dt} which can be expressed in a simpler way : e = - N S\frac{\mathrm dB}{\mathrm dt} by assuming that the induced magnetic field B is homogeneous over a surface S (the magnetic flux will be expressed \Phi = B \times S ).

The induced voltage (e) may be increased several ways:

• increase the surface (S),
• increase the turn number (N),
• use a ferromagnetic core.

Search coil using a ferromagnetic core

When a coil is wound around a ferromagnetic core, that increases the sensitivity of the sensor thanks to the apparent permeability of the ferromagnetic core.

Apparent permeability

The magnetic amplification, known as apparent permeability \mu_{app}, is the result of the magnetization of the ferromagnetic core response to an external magnetic field. The magnetization is reduced by the demagnetizing field.

: \mu_{app} = \frac{\mu_r}{1 + N_z (\mu_r - 1)}

where \mu_r is the relative permeability, N_z is the demagnetizing coefficient in the z direction.

The induced voltage will be written : -Ne = NS\mu_{app}\frac{N\mathrm dB}{\mathrm dt}

The demagnetizing coefficient can easily be computed in the case of simple shapes (spheres and ellipsoids).

Applications

• Non-destructive testing
• Magnetotellurics
• Space research

References

References

1. (1 March 2007). "Induction coil sensors—a review". Measurement Science and Technology.
2. (2021). "Magnetic sensors and magnetometers". Artech House.
3. Robinson, David A.. (October 1963). "A Method of Measuring Eye Movemnent Using a Scieral Search Coil in a Magnetic Field". Institute of Electrical and Electronics Engineers.
4. (2016). "Spaced-based search coil magnetometers". Journal of Geophysical Research: Space Physics.