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Helmholtz coil, named after the German physicist Hermann von Helmholtz, is consisted of two identical electromagnetic coils place in parallel and aligned their centers in the same axis like a mirror image as shown in Figure 1. When electrical current pass through the coils in the same direction, it creates a highly uniform magnetic field in a 3-

Figure 3. High-

Because the two magnetic coils are designed to be identical, uniform magnetic field is achieved when the coil radius is equal to the separation distance. The two coils are connected in series such that identical current is feeding both coils will create two identical magnetic fields. The two added fields achieved uniform magnetic field in a cylindrical volume of space in the center between the two parallel coils. This cylindrical-

Helmholtz electromagnetic field is generated by either using Alternating Current (AC) or Direct Current (DC). Majority of Helmholtz coils used for scientific experiments generate static (constant) magnetic fields. Static magnetic field uses Direct Current. In some test and measurement applications require non-

The magnetic field inside the coils is given below.

Eq. 1

B = field in Tesla

n = number of turns in a coil

I = current in amperes

R = coil radius in meters

Techniques for Producing High-

A self-

Figure 2. A pair of Helmholtz coils are modeled as two inductors and two resistors in series.

A set of coils can be modeled as shown in Figure 2. Each coil is modeled as a parasitic resistor connected to an inductor in series. The parasitic resistor's resistance is typically very small. For most Helmholtz coil test cases in which the testing frequency is far lower than the self-

If the Helmholtz coil testing frequency is high-

Figure 4. Waveform amplifier directly drives the coils.

There are three ways to generate high-

The Helmholtz coils may be driven directly using a current amplifier driver such as the T250 Waveform Amplifier. The direct-

Figure 5. Circuit representation of amplifier directly drives the a pair of Helmholtz coils.

The magnetic field is calculated in the above using Equation 1. The minimum needed voltage to produce the required current can be calculated using Equation 2. Higher inductance (or resistance) or frequency will require higher voltage. For that reason, it is important to design low inductance AC Helmholtz coils. The next step is to drive the Helmholtz coil pair with a high-

I is the peak current

is the angular frequency, = 2πf

L1 + L2 are the total inductance,

R1 + R2 are the total resistance.

In some scientific experiments, the required electromagnetic field is at high frequency in the range of hundreds of kilo-

Equation 2

After calculating the current and voltage from equation 1 and 2 discussed above, use the Table 1 to select the amplifier model.

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Resources for Helmholtz Coil Design

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Figure 7. Circuit representation of the Helmholtz coils in resonance using a series capacitor.

As illustrated in Figure 6 and 7, to operate the high frequency Helmholtz coils in resonance mode, a series capacitor is added. The reactance of the series capacitor has an opposite polarity to the inductor. Thus, the capacitor is acting to cancel the reactance. Hence the total impedance is reduced. At resonance the capacitor reactance (imaginary part of the impedance) fully cancels the inductor reactance. That is, the reactance of the inductor and the capacitor have equal magnitude but complete opposite polarity. Only the inductor's (and capacitor's) parasitic resistance remains. With only the resistance remaining, even at high frequency the function generator amplifier can drive high current through the Helmholtz coils. This resonant method permits the signal amplifier to drive high current through the high-

Equation-

Equation 3

Equation 4

Figure 6. The current amplifier drives high current through the Helmholtz coils using a series capacitor.

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