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Search coil magnetometer

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Thesearch coil magnetometer orinduction magnetometer, based on aninductive sensor (also known asinductive loop and inductive coil), is amagnetometer which measures the varyingmagnetic flux. An inductive sensor connected to a conditioningelectronic circuit constitutes a search coil magnetometer. It is avector 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.

Principle

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The inductive sensor is based onFaraday's law of induction. The temporal variation of themagnetic fluxΦ{\displaystyle \Phi } through aN turns circuit will induce a voltagee{\displaystyle e} which follows

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

which can be expressed in a simpler way

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

by assuming that the induced magnetic fieldB is homogeneous over a surfaceS (themagnetic flux will be expressedΦ=B×S{\displaystyle \Phi =B\times S}).

Figure 1: Induction sensor made up of a winding (orange) surrounding a ferromagnetic core (grey)

The induced voltage (e{\displaystyle 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

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

Apparent permeability

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The magnetic amplification, known as apparent permeabilityμapp{\displaystyle \mu _{app}}, is the result of themagnetization of the ferromagnetic core response to an external magnetic field. The magnetization is reduced by the demagnetizing field.

μapp=μr1+Nz(μr1){\displaystyle \mu _{app}={\frac {\mu _{r}}{1+N_{z}(\mu _{r}-1)}}}

whereμr{\displaystyle \mu _{r}} is therelative permeability,Nz{\displaystyle N_{z}} is the demagnetizing coefficient in thez direction.

The induced voltage will be written

Ne=NSμappNdBdt{\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).

Applications

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References

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See also

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