Reels of Helmholtz

The reels of Helmholtz , of the name of Hermann Ludwig von Helmholtz, are a device made up of two reels circular of the same ray, parallels, and placed one opposite the other at a distance equal to their ray. While making circulate Electric current in these reels, a Magnetic field is created in their vicinity which with the characteristic to be relatively uniform in the center of the device in a volume smaller than the reels themselves.

This type of reels is often used in physics to create relatively weak magnetic fields quasi-uniforms with little material. One can for example make use of it to eliminate the Terrestrial magnetic field so that it does not disturb the experiment.

Theory

One can model the reels of Helmholtz by two associations of N whorls traversed by the same current I , same rays R , and separated from a distance R (see Champ of a whorl of current).

The complete shape of the magnetic field is rather complicated (see figure opposite), but one can calculate his expression, via the law of Biot and Savart, on the axis of the reels starting from the field created by a reel for any point of this axis, at a distance X of its center:

$B\_1\; (X)\; =\; \backslash \; frac\; \{\backslash \; mu\_0\; N\; I\; R^2\}\; \{2\; (R^2+x^2)\; ^\; \{3/2\}\}$

where $\backslash \; mu\_0$ is the magnetic Perméabilité of the vacuum.

To calculate the value of the magnetic field in the center of the device, one makes the sum of the fields created in this point by each reel, one uses in fact the theorem of superposition, theorem of which the use is validated by the linearity of the Maxwell's equations:

$B\; =\; B\_1\; (R/2)\; +\; B\_1\; (-\; R/2)\; =\; \backslash \; left\; (\backslash \; frac\; \{4\}\; \{5\}\; \backslash \; right)\; ^\; \{3/2\}\; \backslash \; frac\; \{\backslash \; mu\_0ni\}\; \{R\}$.

One can thus notice that the field increases if one adds current or whorls, but which it decreases if the reels are moved away.

Reels of laboratory

The typical characteristics of these reels are: R ~ 10 cm, I ~ 1 has, N ~ 10. The magnetic field obtained in the center is worth thus approximately $10^\; \{-\; 4\}$ T, which corresponds to the terrestrial magnetic field.

A way of obtaining a magnetic field of a better uniformity is to use a Solénoïde, but it presents the disadvantage of being more cumbersome than the reels of Helmholtz, and thus sometimes impossible to use.

To obtain more intense magnetic fields, it is necessary to use more expensive material like a electromagnet.

See too

• Magnetostatic

External bonds

• Leybold Didactic GMBH

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