origin is an inflection point for the field strength due to each coil separately, one can guarantee that the order term is also zero, and hence the leading non-constant term is of order . The inflection point for a simple coil is located along the coil axis at a distance from its centre. Thus the locations for the two coils are . The calculation detailed below gives the exact value of the magnetic field at the center point. If the radius is R, the number of turns in each coil is n and the current through the coils is I, then the magnetic field B at the midpoint between the coils will be given by where is the permeability of free space . Derivation Start with the formula for the on-axis field due to a single wire loop which is itself derived from the Biot–Savart law: Here = the permeability constant = = coil current, in amperes, = coil radius, in meters, = coil distance, on axis, to point, in meters, is the distance dependent, dimensionless coefficient. 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: For , the distance coefficient can be expanded in Taylor series as:In a Helmholtz pair, the two coils are located at , so the B-field strength at any would be: The points near the center (halfway between the two coils) have , and the Taylor series of is:.In an anti-Helmholtz pair, the B-field strength at any would be: The points near the center (halfway between the two coils) have , and the Taylor series of is:. Time-varying magnetic field 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