# Focusing a beam of ions

**Electricity and Magnetism**Level 4

A source of ions at point O produces a slightly diverging beam with half-angle of divergence \(\alpha_{0}\ll 1.\) In order to collimate (re-focus) the beam, one can apply a uniform magnetic field along the z-axis (see the figure below). If all the ions have the same initial velocity and specific charge \( \frac{q}{m}\), the beam focuses at point A, again at point 2A and so on. Assuming that \(\frac{q}{m}= 10^{5}~\mbox{C/kg} \), \( B=10^{-3}~\mbox{T} \), and \(v=100~\mbox{m/s}\), find the distance \(\overline{\mbox{OA}}\) **in meters**.

**Your answer seems reasonable.**Find out if you're right!

**That seems reasonable.**Find out if you're right!

Already have an account? Log in here.