Solution to 2008 Problem 71

Setting the centripetal force equal to the Lorentz force gives
\begin{align*}m_e \frac{v^2}{r} = e v B\end{align*}
This can then be solved for v:
\begin{align*}v = \frac{e B r}{m_e}\end{align*}
So, if r_1/r_2 = 1/3, then
\begin{align*}\frac{v_1}{v_2} = \frac{e B r_1/m_e}{e B r_2/m_e} = \frac{r_1}{r_2} = \boxed{\frac{1}{3}}\end{align*}
Therefore, answer (B) is correct.

return to the 2008 problem list

return to homepage

Please send questions or comments to where X = physgre.