Difference between revisions of "Radius of Curvature Calculation"

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<math>r = \frac{\rho}{q*B}</math>
 
<math>r = \frac{\rho}{q*B}</math>
 +
 +
To get the momentum of the incident electrons where momentum is <math>\frac{kg*m}{s}</math> the energy of the beam which
  
 
For this sample equation 1 MeV will be used to determine the radius of curvature per MeV of the incident beam.
 
For this sample equation 1 MeV will be used to determine the radius of curvature per MeV of the incident beam.
  
Energy = 1 MeV
+
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
 
Magnetic Field (B) = 0.35 Tesla
  
Charge of an electron = <math>1.6022 * 10^{19} C</math>
+
Charge of an electron = <math>1.6022 * 10^{19} Coulombs</math>

Revision as of 08:37, 17 February 2009

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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]

To get the momentum of the incident electrons where momentum is [math]\frac{kg*m}{s}[/math] the energy of the beam which

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

Charge of an electron = [math]1.6022 * 10^{19} Coulombs[/math]