Radius of Curvature Calculation: Difference between revisions
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[http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back] | [http://wiki.iac.isu.edu/index.php/PhotoFission_with_Polarized_Photons_from_HRRL Go Back]Below are my calculations done for determining the radius of curvature of an electron/positron in the magnetic field for the pair spectrometer.The Lorentz force is the centripetal force acting upon the electron/positron in the magnetic field which gives the following equation.<math>\frac{(m*v^2)}{r} = q * v * B </math>This equation can be rearranged to solve for r (and given that mv = momentum) to give the following equation<math>r = \frac{\rho}{q*B}</math>For this sample equation 1 MeV will be used to determine the radius of curvature per MeV of the incident beam.Energy = 1 MeV = <math> 1 * 10^6 \frac{J}{C} * 1.6022 * 10^{-19}C = 1*10^6\frac{kg * m^2}{s^2 * C} * 1.6022 * 10^{-19}C </math>Magnetic Field (B) = 0.35 Tesla = <math>0.35\frac{kg}{C*s}</math>Charge of an electron (q) = <math>1.6022 * 10^{19} Coulombs</math>To get the momentum of the positron/electron the energy of the particle is divided by the speed of the particle (ie <math> 2.99 * 10^8 \frac{m}{s})</math>Substituting the numbers above into the radius equation gives the following<math> \frac{(1*10^6 \frac{kg*m^2}{s^2*C}) * (1.6022 * 10^{-19}C)}{(2.99*10^8\frac{m}{s})*(0.35\frac{kg}{C*s})*(1.6022 * 10^{-19}C)}</math> | ||
Below are my calculations done for determining the radius of curvature of an electron/positron in the magnetic field for the pair spectrometer. | |||
The Lorentz force is the centripetal force acting upon the electron/positron in the magnetic field which gives the following equation. | |||
<math>\frac{(m*v^2)}{r} = q * v * B </math> | |||
This equation can be rearranged to solve for r (and given that mv = momentum) to give the following equation | |||
<math>r = \frac{\rho}{q*B}</math> | |||
For this sample equation 1 MeV will be used to determine the radius of curvature per MeV of the incident beam. | |||
Energy = 1 MeV = <math> 1 * 10^6 \frac{J}{C} * 1.6022 * 10^{-19}C = 1*10^6\frac{kg * m^2}{s^2 * C} * 1.6022 * 10^{-19}C </math> | |||
Magnetic Field (B) = 0.35 Tesla = <math>0.35\frac{kg}{C*s}</math> | |||
Charge of an electron (q) = <math>1.6022 * 10^{19} Coulombs</math> | |||
To get the momentum of the positron/electron the energy of the particle is divided by the speed of the particle (ie <math> 2.99 * 10^8 \frac{m}{s})</math> | |||
Substituting the numbers above into the radius equation gives the following | |||
<math> \frac{(1*10^6 \frac{kg*m^2}{s^2*C}) * (1.6022 * 10^{-19}C)}{(2.99*10^8\frac{m}{s})*(0.35\frac{kg}{C*s})*( | |||
1.6022 * 10^{-19}C)}</math> | |||
Revision as of 08:50, 17 February 2009
Go BackBelow are my calculations done for determining the radius of curvature of an electron/positron in the magnetic field for the pair spectrometer.The Lorentz force is the centripetal force acting upon the electron/positron in the magnetic field which gives the following equation.[math]\displaystyle{ \frac{(m*v^2)}{r} = q * v * B }[/math]This equation can be rearranged to solve for r (and given that mv = momentum) to give the following equation[math]\displaystyle{ r = \frac{\rho}{q*B} }[/math]For this sample equation 1 MeV will be used to determine the radius of curvature per MeV of the incident beam.Energy = 1 MeV = [math]\displaystyle{ 1 * 10^6 \frac{J}{C} * 1.6022 * 10^{-19}C = 1*10^6\frac{kg * m^2}{s^2 * C} * 1.6022 * 10^{-19}C }[/math]Magnetic Field (B) = 0.35 Tesla = [math]\displaystyle{ 0.35\frac{kg}{C*s} }[/math]Charge of an electron (q) = [math]\displaystyle{ 1.6022 * 10^{19} Coulombs }[/math]To get the momentum of the positron/electron the energy of the particle is divided by the speed of the particle (ie [math]\displaystyle{ 2.99 * 10^8 \frac{m}{s}) }[/math]Substituting the numbers above into the radius equation gives the following[math]\displaystyle{ \frac{(1*10^6 \frac{kg*m^2}{s^2*C}) * (1.6022 * 10^{-19}C)}{(2.99*10^8\frac{m}{s})*(0.35\frac{kg}{C*s})*(1.6022 * 10^{-19}C)} }[/math]