Helmholtz coil
A Helmholtz coil is a device for producing a region of nearly uniform magnetic field, named after the German physicist Hermann von Helmholtz.
It consists of two electromagnets on the same axis, carrying an equal electric current in the same direction.
A Helmholtz pair consists of two identical circular magnetic coils that are placed symmetrically along a common axis, one on each side of the experimental area, and separated by a distance
Each coil carries an equal electric current in the same direction.
, which is what defines a Helmholtz pair, minimizes the nonuniformity of the field at the center of the coils, in the sense of setting
as explained below), but leaves about 7% variation in field strength between the center and the planes of the coils.
reduces the difference in field between the center and the planes of the coils, at the expense of worsening the field's uniformity in the region near the center, as measured by
[3] In some applications, a Helmholtz coil is used to cancel out the Earth's magnetic field, producing a region with a magnetic field intensity much closer to zero.
[4] The calculation of the exact magnetic field at any point in space is mathematically complex and involves the study of Bessel functions.
Things are simpler along the axis of the coil-pair, and it is convenient to think about the Taylor series expansion of the field strength as a function of
, the distance from the central point of the coil-pair along the axis.
is an inflection point for the field strength due to each coil separately, one can guarantee that the order
The calculation detailed below gives the exact value of the magnetic field at the center point.
Start with the formula for the on-axis field due to a single wire loop which is itself derived from the Biot–Savart law:[5] Here The Helmholtz coils consists of n turns of wire, so the equivalent current in a one-turn coil is n times the current I in the n-turn coil.
Substituting nI for I in the above formula gives the field for an n-turn coil:
.Most Helmholtz coils use DC (direct) current to produce a static magnetic field.
Many applications and experiments require a time-varying magnetic field.
These applications include magnetic field susceptibility tests, scientific experiments, and biomedical studies (the interaction between magnetic field and living tissue).
The required magnetic fields are usually either pulse or continuous sinewave.
The magnetic field frequency range can be anywhere from near DC (0 Hz) to many kilohertz or even megahertz (MHz).
An AC Helmholtz coil driver is needed to generate the required time-varying magnetic field.
The waveform amplifier driver must be able to output high AC current to produce the magnetic field.
Use the above equation in the mathematics section to calculate the coil current for a desired magnetic field, B. where
Then calculate the required Helmholtz coil driver amplifier voltage:[6] where Generating a static magnetic field is relatively easy; the strength of the field is proportional to the current.
Generating a high-frequency magnetic field is more challenging.
The coils are inductors, and their impedance increases proportionally with frequency.
To provide the same field intensity at twice the frequency requires twice the voltage across the coil.
The capacitance is chosen to resonate the coil at the desired frequency.
[6] When the pair of two electromagnets of a Helmholtz coil carry an equal electric current in the opposite direction, it is known as anti-Helmholtz coil, which creates a region of nearly uniform magnetic field gradient, and is used for creating magnetic traps for atomic physics experiments.
can reduce the variance of the field on the axis to zero up to the sixth derivative of position.
