Encyclopedia Magnetica™

Stan Zurek, Calculator of H along the axis of a Helmholtz coil, Encyclopedia Magnetica,
https://e-magnetica.pl/doku.php/calculator/helmholtz_coil, {accessed: 2025-02-10}

Magnetic field strength H at the axis of a Helmholtz coil
Source: [1] B.D. Cullity, C.D. Graham, Introduction to Magnetic Materials, 2nd edition, Wiley, IEEE Press, New Jersey, 2009, ISBN 9780471477419
[1], eq. (2.4),(2.5), p. 26	$$ H_{centre}(t) = \frac{N_{half}·I (t)· 8 } {r·5·\sqrt{5}} \approx 0.71554·\frac{N_{half}·I}{r} $$	(A/m)
where: $I(t)$ - current (A) at time $t$ (s), $N_{half}$ - number of turns (unitless) of each half-coil, $r$ - radius (m)

Current I = Radius r = Choose option: Number of turns N = (unitless) Position along the axis x = (x = 0 means centre of the system) *H(x)* = *B(x)* (μ₀) =
Notes: This equation is valid only for infinitely “thin” coils. The instantaneous values of H are directly proportional to the instantaneous values of I. The value of B(μ₀) is for vacuum (i.e. non-magnetic medium). Both halves are assumed to be connected in series (for uniform field).

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