Difference between revisions of "Magnet"

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Current: <math>138 A</math>
 
Current: <math>138 A</math>
  
Resistance:  <math>0.116 ohm</math>
+
Resistance:  <math>0.116 Ohm</math>
  
 
Voltage: <math>V=IR=16.008 V</math>
 
Voltage: <math>V=IR=16.008 V</math>

Latest revision as of 18:05, 22 May 2009

Specs:

TESLA ENGINEERING: 7 Degree Bend Angle Dipole

Bmax=0.35T

Current: 138A

Resistance: 0.116Ohm

Voltage: V=IR=16.008V

Water Flow: 1.2L/minute


CALCULATIONS

Radius of Curvature


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.

(mv2)r=qvB

This equation can be rearranged to solve for r (and given that mv = momentum) to give the following equation

r=ρqB

For this sample equation 1 MeV will be used to determine the radius of curvature per MeV of the incident beam.

Energy = 1 MeV = 1106JC1.60221019C=1106kgm2s2C1.60221019C

Magnetic Field (B) = 0.35 Tesla = 0.35kgCs

Charge of an electron (q) = 1.60221019Coulombs

To get the momentum of the positron/electron the energy of the particle is divided by the speed of the particle (ie 2.99108ms)

Substituting the numbers above into the radius equation gives the following

(1106kgm2s2C)(1.60221019C)(2.99108ms)(0.35kgCs)(1.60221019C)=0.009556meters=0.9556cm

So basically the radius of curvature for the electrons/positrons is ~0.9556cm per MeV

So for a 7 MeV electron/positron pair the radius of curvature for either particle in a 0.35 T field would be 6.69cm



Calculating the Magnetic Field Needed:

Lorentz Force equation: F=q(v×B)

Electron moves through the magnetic field B accelerated by force F proportional to the component of velocity perpendicular to the field B and velocity v. Moves with constant kinetic energy and speed due to the fact that the magnetic field never does work on the particle since the always moves perpendicular to the force.

Magnetic force: F=evB

The radius of the arc can be through: (mv2)/R=evB

giving: R=mv/eB

The length of the circular arc is S and the deflection angle is found as: sin(θ)=S/R

For small θ, and large R, the arc length S will be approx L, giving: sin(θ)=L/R=L*e*B/m*v

Giving θ=sin^(-1)(c*B*L/p)

The displacement is found as: d=R-R*cos(θ)=m*v/e*B*(1-cos(θ))

Table: Data for B=0.0078 T.

Momentum Radius of Curvature Bend Angle Bend Angle Displacement @ end of magnet
P (MeV) R (m) θ (radians) θ (degrees) d (cm)
1 0.43 0.70 40.02 10.01
2 0.86 0.33 18.76 4.54
3 1.28 0.22 12.38 2.98
4 1.71 0.16 9.25 2.22
5 2.14 0.13 7.39 1.78
6 2.57 0.11 6.15 1.48
7 2.99 0.09 5.27 1.27
8 3.42 0.08 4.61 1.11
9 3.85 0.07 4.10 0.98
10 4.28 0.06 3.69 0.89
11 4.70 0.06 3.35 0.80
12 5.13 0.05 3.07 0.74
13 5.56 0.05 2.84 0.68
14 5.99 0.05 2.63 0.63
15 6.41 0.04 2.46 0.59
16 6.84 0.04 2.30 0.55



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