# Runge-kutta method for a force acting upon a charged particle

by superstrings
Tags: acting, charged, force, method, particle, rungekutta
 HW Helper Thanks P: 989 Acceleration is the second derivative of position (x) with respect to time. The first derivative is velocity (v). It follows that acceleration is the derivative of velocity. Thus, as a first order ODE, F = ma becomes $$\frac {dv}{dt} = F(x,v)/m = (q/m)(E + v \times B) \\ \frac{dx}{dt} = v$$ At this point you can use Runge-Kutta.