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Helmholtz Coil Field at Arbitrary Distance

A Helmholtz coil is a device for producing a region of nearly uniform magnetic field. It consists of two solenoid electromagnets on the same axis.

The magnetic flux density increases directly with the current and the number of coils. The magnetic flux density decreases with the radii of the coils. As the distance from the center of the Helmholtz coils increases, the field strength first increases (as it approaches the coil radius) and then declines.

Formula

QuantityVariable["B", "MagneticFluxDensity"] == Quantity[1/2, "MagneticConstant"]*QuantityVariable["I", "ElectricCurrent"]*QuantityVariable["N", "Unitless"]*QuantityVariable["R", "Radius"]^2*(((-QuantityVariable["d", "Distance"] + QuantityVariable["R", "Radius"]/2)^2 + QuantityVariable["R", "Radius"]^2)^(-3/2) + ((QuantityVariable["d", "Distance"] + QuantityVariable["R", "Radius"]/2)^2 + QuantityVariable["R", "Radius"]^2)^(-3/2))

symbol description physical quantity
B magnetic flux density "MagneticFluxDensity"
I electric current "ElectricCurrent"
N coil turns "Unitless"
R radius "Radius"
d distance from center "Distance"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Helmholtz Coil Field at Arbitrary Distance"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Helmholtz Coil Field at Arbitrary Distance"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Helmholtz Coil Field at Arbitrary Distance"], {QuantityVariable[ "N","Unitless"] -> 1}]
Out[3]=

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