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]

CALCULATIONS

Calculating the Magnetic Field Needed:

Lorentz Force equation: [math]F=q(v×B)[/math]

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=evB[/math]

The radius of the arc can be through: [math](mv^2)/R=evB[/math]

giving: [math]R=mv/eB[/math]

The length of the circular arc is S and the deflection angle is found as: [math]sinθ=S/R[/math]

For small θ, and large R, the arc length S will be approx L, giving: [math]sinθ=L/R=LeB/mv[/math] Giving [math]θ=sin^(-1)⁡〖 (cBL/p)〗[/math] The displacement is found as: [math]d=R-Rcosθ=mv/eB(1-cosθ)[/math]

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

Go Back