QuickField

A new approach to field modelling
 Language: Global English Deutch Espanol Francais Italiano Danmark Ceske Chinese Pycckuü

order

evaluation

editions

version history

packages

components

programming

consulting

industrial

educational

scientific

sample problems

success stories

customers

 webinars virtual classroom online courses customer login glossary quickfield help faq
 quickfield student edition user manual data libraries video free tools
 product news events blog publications subscription

>> >>

# Charged particle trajectory in the uniform static magnetic field. Case: plane-parallel.

Problem Type:
Plane-parallel problem of DC magnetics.

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

Problem:
Calculate charged particle trajectory in magnetic field neglecting relativistic effects.

Solution:
The analytical solution gives spiral trajectory.
Radius in YZ-plane RYZ = vy / Bx * m/q [m].
Period T = 2π / Bx * m/q [s].
Lorentz force Fz = q*vy*Bx [N].

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

Results:

Analytical solution:
Radius in YZ-plane RYZ = (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 Fz = 1.602e-19 * 5e6 * 0.04 = 3.20e-15 N.

TrajectoryTracer tool:
Radius in YZ-plane RYZ = 0.14215/2 = 0.00711 m.
Period T = 4.47e-9*2 = 8.94e-9 s.
Lorentz force Fz = 3.20e-15 N. • Video: