An electron of charge and mass moves in the -plane in a uniform magnetic field with

PHYSICS · Subjective · Fermi University Physics · Computational Physics · Electricity, Magnetism & Electromagnetism · Simulating classical dynamical systems

Computational Physics, Ch Stepping the equations of motion: four integrators measured

Problem

An electron of charge q=−1.6×10−19 Cq = -1.6\times10^{-19}\,\mathrm{C} and mass m=9.11×10−31 kgm = 9.11\times10^{-31}\,\mathrm{kg} moves in the xyxy-plane in a uniform magnetic field B=Bz^\mathbf{B} = B\hat{\mathbf{z}} with B=0.50 TB = 0.50\,\mathrm{T}. The magnetic force is F=qv×B\mathbf{F} = q\mathbf{v}\times\mathbf{B}, which gives mv˙x=qBvym\dot v_x = qBv_y and mv˙y=−qBvxm\dot v_y = -qBv_x. (a) Write the motion as a first-order system: give the four-component state vector y=(x,y,vx,vy)\mathbf{y} = (x,y,v_x,v_y) and f(y)\mathbf{f}(\mathbf{y}). (b) Evaluate f\mathbf{f} numerically at x=y=0x=y=0, vx=2.0×105 m s−1v_x = 2.0\times10^5\,\mathrm{m\,s^{-1}}, vy=0v_y = 0.

Browse the problem library