Wolfram Computation Meets Knowledge

Wolfram Formula Repository (Under Development)

Cherenkov Radiation

Cherenkov radiation is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium.

The Cherenkov angle equals the inverse cosine of the speed of light in a vacuum divided by the index of refraction of the medium and the velocity of the particle in the medium.

Formula

{QuantityVariable["γ", "RelativisticGamma"] == 1 + (Quantity[1, "SpeedOfLight"^(-2)]*QuantityVariable["K", "Energy"])/QuantityVariable["m", "Mass"], QuantityVariable[Subscript["v", "p"], "Speed"] == Quantity[1, "SpeedOfLight"]*Sqrt[1 - QuantityVariable["γ", "RelativisticGamma"]^(-2)], QuantityVariable["θ", "Angle"] == ArcCos[Quantity[1, "SpeedOfLight"]/(QuantityVariable["n", "Unitless"]*QuantityVariable[Subscript["v", "p"], "Speed"])], QuantityVariable[Subscript["c", "m"], "Speed"] == Quantity[1, "SpeedOfLight"]/QuantityVariable["n", "Unitless"]}

symbol description physical quantity
γ relativistic gamma "RelativisticGamma"
K kinetic energy of particle "Energy"
m mass of particle "Mass"
vp velocity of particle in medium "Speed"
θ Cherenkov angle "Angle"
n refractive index of medium "Unitless"
cm light speed in medium "Speed"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Cherenkov Radiation"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Cherenkov Radiation"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Cherenkov Radiation"], {QuantityVariable["\[Theta]","Angle"] -> Quantity[0.512273`, "Radians"], QuantityVariable[ \!\(\*SubscriptBox[\("v"\), \("p"\)]\),"Speed"] -> Quantity[2.58783`*^8, ("Meters")/("Seconds")]}]
Out[3]=

Source Metadata

  • Creator:
  • Contributor:

Publisher Information