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Maximal Magnetic Induction in a Circular Coil

Magnetic induction is the production of an electromotive force across an electrical conductor due to its dynamic interaction with a magnetic field.

The maximal magnetic induction in a circular coil increases directly with current and the number of coils. As the distance between the inner and outer coil radius increases, so does the induction.

Formula

QuantityVariable["B", "MagneticInduction"] == (Log[(2*QuantityVariable["R", "Radius"] + QuantityVariable["r", "Radius"]*Sqrt[(QuantityVariable["l", "Length"]^2 + 4*QuantityVariable["R", "Radius"]^2)/QuantityVariable["r", "Radius"]^2])/((2 + Sqrt[4 + QuantityVariable["l", "Length"]^2/QuantityVariable["r", "Radius"]^2])*QuantityVariable["r", "Radius"])]*Quantity[1/2, "MagneticConstant"]*QuantityVariable["I", "ElectricCurrent"]*QuantityVariable["N", "Unitless"])/(-QuantityVariable["r", "Radius"] + QuantityVariable["R", "Radius"])

symbol description physical quantity
B magnetic induction "MagneticInduction"
l coil length "Length"
r inner coil radius "Radius"
R outer coil radius "Radius"
I electric current "ElectricCurrent"
N coil turns "Unitless"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Maximal Magnetic Induction in a Circular Coil"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject["Maximal Magnetic Induction in a Circular Coil"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Maximal Magnetic Induction in a Circular Coil"], {QuantityVariable[ "l","Length"] -> Quantity[2.`, "Centimeters"], QuantityVariable["r","Radius"] -> Quantity[1.`, "Centimeters"], QuantityVariable["B","MagneticInduction"] -> None, QuantityVariable["I","ElectricCurrent"] -> Quantity[1.`, "Amperes"], QuantityVariable["N","Unitless"] -> 100}]
Out[3]=

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