Big Red

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]

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Calculations:

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: (mv^2)/R=evB

giving R=mv/eB 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 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. Momentum Radius of Curvature 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

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