text b we will start by analysing equation 1 2 first we define omega p

Question

\text { (b) We will start by analysing Equation 1.2. First, we define } \Omega=\phi \text { and } V=\dot{r} Show that Equation 1.2 can be re-written as: r \frac{d \Omega}{d r}+2 \Omega=\frac{e B}{m} Use an integrating factor to integrate this expression and by applyingthe initial conditions, show that: \Omega=\frac{B e}{2 m}\left(1-\frac{r_{0}^{2}}{r^{2}}\right)