Difference between revisions of "Big Red"

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== Specs: ==
 
== Specs: ==
  
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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.  
 
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
+
Magnetic force: <math>F=e*v*B</math>
 +
 
 +
The radius of the arc can be through: <math>(m*v^2)/R=e*v*B</math>
 +
 
 +
giving: <math>R=m*v/e*B</math>
 +
 
 +
The length of the circular arc is  S and the deflection angle is found as: sin(θ)=S/R
  
−
The radius of the arc can be through: (mv^2)/R=evB
+
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 R=mv/eB
+
Giving    θ=sin^(-1)(c*B*L/p)
−
The length of the circular arc is  S and the deflection angle is found as sinθ=S/R 
 
  
−
For small  θ, and large R, the arc length  S will be approx L, giving
+
The displacement is found as: d=R-R*cos(θ)=m*v/e*B*(1-cos(θ))
−
sinθ=L/R=LeB/mv   
 
−
Giving    θ=sin^(-1)⁡〖 (cBL/p)〗
 
−
The displacement is found as: d=R-Rcosθ=mv/eB(1-cosθ)  
 
  
−
Table:  Data for  B=0.0015 T.
+
Table:  Data for  B=0.0078 T.
 
{| border="1" cellpadding="2"
 
{| border="1" cellpadding="2"
 
!width="70"|Momentum
 
!width="70"|Momentum
 
!width="70"|Radius of Curvature
 
!width="70"|Radius of Curvature
−
!width="140"|Bend Angle
+
!width="70"|Bend Angle
 +
!width="70"|Bend Angle
 
!width="70"|Displacement @ end of magnet
 
!width="70"|Displacement @ end of magnet
  
Line 47: Line 49:
 
|P (MeV)||R (m)||θ (radians)||θ (degrees)||d (cm)
 
|P (MeV)||R (m)||θ (radians)||θ (degrees)||d (cm)
 
|-
 
|-
−
|1||2.22376032||0.12398179||7.103633471||1.706936726
+
|1||0.43||0.70||40.02||10.01
 
|-
 
|-
−
|2||4.44752065||0.06187167||3.544985606||0.851006969
+
|2||0.86||0.33||18.76||4.54
 
|-
 
|-
−
|3||6.67128097||0.04123315||2.362485567||0.567036176
+
|3||1.28||0.22||12.38||2.98
 
|-
 
|-
−
|4||8.89504129||0.03092103||1.77164444||0.425198022
+
|4||1.71||0.16||9.25||2.22
 
|-
 
|-
−
|5||11.1188016||0.0247354||1.417234227||0.340129141
+
|5||2.14||0.13||7.39||1.78
 
|-
 
|-
−
|6||13.3425619||0.02061219||1.180991717||0.283427701
+
|6||2.57||0.11||6.15||1.48
 
|-
 
|-
−
|7||15.5663223||0.01766726||1.012259595||0.242931183
+
|7||2.99||0.09||5.27||1.27
 
|-
 
|-
−
|8||17.7900826||0.01545867||0.885716346||0.212560897
+
|8||3.42||0.08||4.61||1.11
 
|-
 
|-
−
|9||20.0138429||0.01374092||0.787296837||0.18894065
+
|9||3.85||0.07||4.10||0.98
 
|-
 
|-
−
|10||22.2376032||0.01236676||0.708562916||0.17004506
+
|10||4.28||0.06||3.69||0.89
 
|-
 
|-
−
|11||24.4613636||0.01124246||0.644145256||0.154585392
+
|11||4.70||0.06||3.35||0.80
 
|-
 
|-
−
|12||26.6851239||0.01030555||0.590464498||0.141702561
+
|12||5.13||0.05||3.07||0.74
 
|-
 
|-
−
|13||28.9088842||0.00951279||0.545042725||0.13080185
+
|13||5.56||0.05||2.84||0.68
 
|-
 
|-
−
|14||31.1326445||0.00883329||0.50611005||0.121458483
+
|14||5.99||0.05||2.63||0.63
 
|-
 
|-
−
|15||33.3564048||0.00824439||0.472368588||0.113360965
+
|15||6.41||0.04||2.46||0.59
 
|-
 
|-
−
|16||35.5801652||0.0077291||0.442844944||0.106275686
+
|16||6.84||0.04||2.30||0.55
 
|}
 
|}
  

Latest revision as of 21:20, 15 May 2009

Specs:

TESLA ENGINEERING: 7 Degree Bend Angle Dipole

[math]B=0.35 T[/math]

Current: [math]138 A[/math]

Resistance: [math]0.116 ohm[/math]

Voltage: [math]V=IR=16.008 V[/math]

Water Flow: [math]1.2 L/minute[/math]


CALCULATIONS

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: [math]F=e*v*B[/math]

The radius of the arc can be through: [math](m*v^2)/R=e*v*B[/math]

giving: [math]R=m*v/e*B[/math]

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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