On-Axis Field
of an Ideal Helmholtz Coil
| These simple formulas use the formula for field due to a current loop to obtain the magnetic field at any point along the axis of an ideal Helmholtz coil. | ||||
Ideal Helmholtz coil in cross section view. |
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| The ideal Helmholtz coil consists of two
coaxial circular current loops with the same radius,
separated from each other by one radius. In other words,
the loops are l apart, such that l = r.
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| Bx
is the magnetic field, in teslas, at any point on the
axis of the Helmholtz coil. The direction of the field is
perpendicular to the plane of the loops. m 0 is the permeability constant (1.26x10-6 H/m) i is the current in the wire, in amperes. r is the radius of the current loops, in meters. g is the ratio, x/r, where x is the distance, on axis, from the center of the Helmholtz coil, and r is the radius of the coil. Note: different units for r may be used as long as the permeability constant is correct for that unit system. |
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| Special
Case: x = 0
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| Bo is the magnetic field, in teslas, at the center of the Helmholtz coil. The direction of the field is perpendicular to the plane of the loops. | ||||
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| The following graph demonstrates the superior central field uniformity of an ideal Helmholtz coil when compared to a solenoid of the same aspect ratio (that is, a solenoid which is as long as its radius): | ||||
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