Difference between revisions of "Big Red"
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'''Calculating the Magnetic Field Needed:''' | '''Calculating the Magnetic Field Needed:''' | ||
| − | Lorentz Force equation: | + | 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. | 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: | + | Magnetic force: F=evB |
The radius of the arc can be through: <math>(mv^2)/R=evB</math> | The radius of the arc can be through: <math>(mv^2)/R=evB</math> | ||
| Line 30: | Line 30: | ||
giving: <math>R=mv/eB</math> | giving: <math>R=mv/eB</math> | ||
| − | The length of the circular arc is S and the deflection angle is found as: <math> | + | The length of the circular arc is S and the deflection angle is found as: <math>sin(theta)=S/R</math> |
| − | For small θ, and large R, the arc length S will be approx L, giving: <math> | + | For small θ, and large R, the arc length S will be approx L, giving: <math>sin(theta)=L/R=LeB/mv</math> |
Giving <math>θ=sin^(-1)〖 (cBL/p)〗</math> | Giving <math>θ=sin^(-1)〖 (cBL/p)〗</math> | ||
| − | The displacement is found as: <math>d=R- | + | The displacement is found as: <math>d=R-Rcos(theta)=mv/eB(1-cos(theta))</math> |
Table: Data for B=0.0015 T. | Table: Data for B=0.0015 T. | ||
Revision as of 22:35, 13 May 2009
Specs:
TESLA ENGINEERING: 7 Degree Bend Angle Dipole
Current:
Resistance:
Voltage:
Water Flow:
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: F=evB
The radius of the arc can be through:
giving:
The length of the circular arc is S and the deflection angle is found as:
For small θ, and large R, the arc length S will be approx L, giving: Giving The displacement is found as:
Table: Data for B=0.0015 T.
| Momentum | Radius of Curvature | Bend Angle | Bend Angle | Displacement @ end of magnet |
|---|---|---|---|---|
| P (MeV) | R (m) | θ (radians) | θ (degrees) | d (cm) |
| 1 | 2.22376032 | 0.12398179 | 7.103633471 | 1.706936726 |
| 2 | 4.44752065 | 0.06187167 | 3.544985606 | 0.851006969 |
| 3 | 6.67128097 | 0.04123315 | 2.362485567 | 0.567036176 |
| 4 | 8.89504129 | 0.03092103 | 1.77164444 | 0.425198022 |
| 5 | 11.1188016 | 0.0247354 | 1.417234227 | 0.340129141 |
| 6 | 13.3425619 | 0.02061219 | 1.180991717 | 0.283427701 |
| 7 | 15.5663223 | 0.01766726 | 1.012259595 | 0.242931183 |
| 8 | 17.7900826 | 0.01545867 | 0.885716346 | 0.212560897 |
| 9 | 20.0138429 | 0.01374092 | 0.787296837 | 0.18894065 |
| 10 | 22.2376032 | 0.01236676 | 0.708562916 | 0.17004506 |
| 11 | 24.4613636 | 0.01124246 | 0.644145256 | 0.154585392 |
| 12 | 26.6851239 | 0.01030555 | 0.590464498 | 0.141702561 |
| 13 | 28.9088842 | 0.00951279 | 0.545042725 | 0.13080185 |
| 14 | 31.1326445 | 0.00883329 | 0.50611005 | 0.121458483 |
| 15 | 33.3564048 | 0.00824439 | 0.472368588 | 0.113360965 |
| 16 | 35.5801652 | 0.0077291 | 0.442844944 | 0.106275686 |