Question

An arrangement of source charges produces electric potential $V=5000\, x^{2}$ along the x-axis, where $V$ is in volt and $x$ is in metre. If a charge particle of mass $1\, g$ and charge $1\, nC$ is present in this field and its turning points are at $\pm 8.0\, cm$, then what is the particle's maximum speed (in $mm / s$ ).

Answer 1

$q V=\frac{1}{2} m v^{2}$
$10^{-9} \times\left(8^{2}-0^{2}\right) \times 5000$
$=\frac{1}{2} \times 10^{-3} \times v^{2}$
$v^{2}=64 \times 10^{-6}$
$\Rightarrow v=8\, mm / s$