Crossed Electric and Magnetic Fields

You are now in a position to apply your chosen algorithm to a more complicated problem. In addition to the uniform magnetic field, $\bi{B}$, we now add an electric field in the $x$-direction, $\bi{E} = (E_x,0,0)$. Thus (1.43a) must be modified to read

$${\d v_x\over \d t} = +\left(q B\over m\right) v_y - \left(\gamma\over m\right) v_x + \left(q E\over m\right)$$ (1.52)

$${\d v_y\over \d t} = -\left(q B\over m\right) v_x - \left(\gamma\over m\right) v_y$$ (1.53)

You should now write a program to solve (1.9.2) using the most appropriate method as found earlier. Try to investigate the behaviour of the system in various physical regimes. You should also vary $\delta t$ to check whether the stability conforms to your expectations. Think about the physical system you are describing and whether your results are consistent with the behaviour you would expect.