Charged particle trajectory in the uniform static magnetic field. Case: cylindrical.

QuickField simulation example

Problem Type
Axisymmetric problem of DC magnetics.

Geometry

Given
Relative permeability of vacuum μ = 1;
External field flux density B_z = -4 mT;
Charge (electron) q = -1.602e-19 C;
Mass (electron) m = 9.109e-31 kg;
Initial velocity (v_x;v_y;v_z) = (0; 5e6; 5e6) m/s.
Emitter position (0; 0; 0).

Task
Calculate charged particle trajectory in magnetic field neglecting relativistic effects.

Solution
The analytical solution gives the spiral trajectory.
Radius in XY-plane R_XY = v_y / B_z * m/q [m].
Period T = 2π / B_z * m/q [s].
Lorentz force F_φ = q*v_y*B_z [N].

To calculate the particle trajectory in QuickField free tool TrajectoryTracer is used.

Results
Analytical solution:
Radius in XY-plane R_XY = (5e6/0.004) * (9.109e-31/1.602e-19) = 0.00711 m.
Period T = (2*3.142/0.04) * (9.109e-31/1.602e-19) = 8.93e-9 s.
Lorentz force F_φ = 1.602e-19 * 5e6 * 0.04 = 3.20e-15 N

TrajectoryTracer tool:
Radius in XY-plane R_XY = 0.14215/2 = 0.00711 m.
Period T = 4.47e-9*2 = 8.94e-9 s.
Lorentz force F_φ = 3.20e-15 N.

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