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Circular Orbit Radius of a Charged Particle in a Magnetic Field

A charged particle moving in a magnetic field will be pushed into a circular path by the interaction of the charge and the magnetic field. The radius of that path can be calculated from the properties of the charge and the magnetic induction.

The radius of the circular orbit of a charged particle in a magnetic field equals the product of the mass and speed of the particle divided by the particle charge and the magnetic induction.

Formula

QuantityVariable["r", "Radius"] == (QuantityVariable["m", "Mass"]*QuantityVariable["v", "Speed"])/(QuantityVariable["B", "MagneticInduction"]*QuantityVariable["q", "ElectricCharge"])

symbol description physical quantity
r radius "Radius"
B magnetic induction "MagneticInduction"
m mass "Mass"
q electric charge "ElectricCharge"
v speed "Speed"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Circular Orbit Radius of a Charged Particle in a \ Magnetic Field"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Circular Orbit Radius of a Charged Particle in a Magnetic Field"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Circular Orbit Radius of a Charged Particle in a Magnetic Field"], \ {QuantityVariable["q","ElectricCharge"] -> Quantity[1.6000000000000002`*^-19, "Coulombs"], QuantityVariable["m","Mass"] -> Quantity[1.671`*^-27, "Kilograms"]}]
Out[3]=

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