A positively charged particle, with charge q, is accelerated by passing through a voltage $V_K$.
The acceleration leaves the charged particle with a kinetic energy $KE = qV_K$. The particle
then approaches a small conducting sphere of radius R, which is at a positive voltage $V_{sphere}$.
The potential energy of the particle at the surface is thus $qV_{sphere}$ (voltage measured relative
to a point far from the sphere, so the electric field from the sphere behaves as if it were caused
by a point charge as long as you are outside the sphere.)
(a) What is the minimum accelerating voltage, $V_{K,min}$, necessary for the particle to
reach the sphere?
(b) What is the cross section for colliding with the sphere? Assume $V_K > V_{K,min}$.
Show your work. Derive your answer by beginning with energy and angular momentum
conservation, and express your answer in terms of R, $V_K$ and $V_{sphere}$.
