Search coil magnetometer

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The search coil magnetometer or induction magnetometer, based on an inductive sensor (also known as inductive loop and inductive coil), is a magnetometer which measures the varying magnetic flux. An inductive sensor connected to a conditioning electronic circuit constitutes a search coil magnetometer. It is a vector magnetometer which can measure one or more components of the magnetic field. A classical configuration uses three orthogonal inductive sensors. The search-coil magnetometer can measure magnetic field from mHz up to hundreds of MHz.

The inductive sensor is based on Faraday's law of induction. The temporal variation of the magnetic flux ${\displaystyle \Phi }$ through a N turns circuit will induce a voltage ${\displaystyle e}$ which follows

${\displaystyle e=-N{\frac {\mathrm {d} \Phi }{\mathrm {d} t}}}$

which can be expressed in a simpler way

${\displaystyle e=-NS{\frac {\mathrm {d} B}{\mathrm {d} t}}}$

by assuming that the induced magnetic field B is homogeneous over a surface S (the magnetic flux will be expressed ${\displaystyle \Phi =B\times S}$).^[1][2]

The induced voltage (${\displaystyle e}$) may be increased several ways:

• increase the surface (S),
• increase the turn number (N),
• use 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.^[1]

The magnetic amplification, known as apparent permeability ${\displaystyle \mu _{app}}$, is the result of the magnetization of the ferromagnetic core response to an external magnetic field. The magnetization is reduced by the demagnetizing field.^[1]

${\displaystyle \mu _{app}={\frac {\mu _{r}}{1+N_{z}(\mu _{r}-1)}}}$

where ${\displaystyle \mu _{r}}$ is the relative permeability, ${\displaystyle N_{z}}$ is the demagnetizing coefficient in the z direction.

The induced voltage will be written

${\displaystyle -Ne=NS\mu _{app}{\frac {N\mathrm {d} B}{\mathrm {d} t}}}$

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

• Eye tracker § Eye-attached tracking^[3]
• Non-destructive testing
• Magnetotellurics
• Space research^[4]

• Waves (Juno) (Uses a magnetic search coil)