Electricity and Magnetism

Motion in Coulomb Potential

Problem by Jong
30 Nov 1999 00:00 WIB

Consider a particle of mass $$m$$, in a Coulomb potential. The equation of motion of particle $m$ could be written as $\frac{d \mathbf{p}}{dt} = -\frac{k}{r^3} \mathbf{r}$. Where $k$ is a positive constant.
a. From the equation of motion write down the conserved quantity $\frac{d\mathbf{B}}{dt} =0$, determine $\mathbf{B}$.

b. Find a second conserved vector $\mathbf{A}$, from $\mathbf{B}$ and angular momentum vector $\mathbf{L}$.