Use the below equation to calculate the Helmholtz field. This equation is for an ideal Helmholtz coil with no wire thickness.
B is the magnetic field in unit of Tesla
n is the number of turns
I is the current in amperes
R is the coil radius in meters
This page is dedicated to provide excellent Helmholtz coil design resources for anyone who wants to design their own coil. We have links to a number of articles for generating high magnetic field even at high frequency. We included resources such as electromagnetic field and inductance calculators. In case you want to buy an off-the-shelf or custom-made coils, we have a link to our Helmholtz coil sale and manufacture list.
Helmholtz field can be produce by using a function generator amplifier like as the TS200 and the TS250. These amplifiers drive high current through coils which generate strong electromagnetic field. You can read the Helmholtz Coil article to learn how to use resonant techniques to produce high-frequency strong electromagnetic field.
This article details several techniques for generating high magnetic field. The first method is directly driving the coil using a current amplifier. The second method is using a series capacitor to resonate with the coil to produce high magnetic field even at high frequency.
This article discusses how to use the series resonant to generate high magnetic field while achieving high frequency. The discussion is for electromagnet in general, but equally applied to Helmholtz field.
A novel technique that uses a special resonant circuit to amplify the current by a factor of two. It is therefore magnify the magnetic field by two. Detail mathematical models are present in this article.