Electrons in a cathode-ray device are accelerated from rest through an initial potential difference \(V_0\) before entering a region containing a uniform magnetic field of magnitude \(B\) directed perpendicular to the electrons' velocity. Inside the magnetic field, the electrons travel along a circular arc of radius \(R_0\). If the accelerating potential difference is increased to \(4V_0\) while the magnetic field magnitude remains unchanged, what is the new radius of curvature of the electron beam's path inside the magnetic field?