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Self-Inductance of a Single-Layer Circular Coil

The self­inductance of a single­layer circular coil is a property that describes the electromotive force caused by the change in current in the coil.

The self\[Hyphen]inductance increases quadratically with the number of coils. It also increases with the coil radius and decreases with the coil length.

Formula

QuantityVariable["L", "MagneticInductance"] == (Quantity[1/3, "MagneticConstant"]*QuantityVariable["N", "Unitless"]^2*QuantityVariable["r", "Radius"]^2*((-8*QuantityVariable["r", "Radius"])/QuantityVariable["l", "Length"] + (QuantityVariable["l", "Length"]^2*Sqrt[1 + (4*QuantityVariable["r", "Radius"]^2)/QuantityVariable["l", "Length"]^2]*(EllipticK[(4*QuantityVariable["r", "Radius"]^2)/(QuantityVariable["l", "Length"]^2*(1 + (4*QuantityVariable["r", "Radius"]^2)/QuantityVariable["l", "Length"]^2))] + EllipticE[(4*QuantityVariable["r", "Radius"]^2)/(QuantityVariable["l", "Length"]^2*(1 + (4*QuantityVariable["r", "Radius"]^2)/QuantityVariable["l", "Length"]^2))]*(-1 + (4*QuantityVariable["r", "Radius"]^2)/QuantityVariable["l", "Length"]^2)))/QuantityVariable["r", "Radius"]^2))/QuantityVariable["l", "Length"]

symbol description physical quantity
L self­inductance "MagneticInductance"
l coil length "Length"
N coil turns "Unitless"
r coil radius "Radius"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Self-Inductance of a Single-Layer Circular Coil"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Self-Inductance of a Single-Layer Circular Coil"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Self-Inductance of a Single-Layer Circular Coil"], \ {QuantityVariable["L","MagneticInductance"] -> Quantity[197.4`, "Nanohenries"], QuantityVariable["N","Unitless"] -> 10}]
Out[3]=

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