Trajectory in an arbitrary electrostatic field
Electricity and Magnetism
Level
5
A charged particle of mass m and charge q moves in an electrostatic field created by an unknown system of static charges. The particle starts from point A with initial velocity is \(v_{1}=1 m/s\) and follows certain trajectory. What should be the velocity (magnitude) \(v_{2}\) in m/s of a particle of mass \(M=10 m\) and charge \(Q=7 q\) at point A in order to follow the same trajectory?
Hint: Compute \[\frac{d}{ds} \frac{\vec{v}}{v},\] where s is the arc length along the trajectory:
\(s=\int_0^t v(t') dt'\).
by
David Mattingly