A proton of mass \(m\) and charge \(+e\) and an alpha particle of mass \(4m\) and charge \(+2e\) are each accelerated from rest through the same electric potential difference \(\Delta V\). Each particle then enters a region of uniform magnetic field \(\vec{B}\) directed perpendicular to its velocity, causing it to travel in a circular arc. What is the ratio of the radius of the circular path of the alpha particle to that of the proton, \(\dfrac{r_\alpha}{r_p}\)?