# Trajectory in an arbitrary electrostatic field

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:

$s=\int_0^t v(t') dt'$.

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