An alpha particle $($a He nucleus, containing two protons and two neutrons and having a mass of traveling horizontally at enters a uniform, vertical, $1\mathrm{.}80$ T magnetic field. $($a$)$What is the diameter of the path followed by this alpha particle? $($b$)$ What effect does the magnetic field have on the speed of the particle? $($c$)$ What are the magnitude and direction of the acceleration of the alpha particle while it is in the magnetic field? $($d$)$ Explain why the speed of the particle does not change even though an unbalanced external force acts on it$.$