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An electron and a proton are each accelerated through the same voltage difference $\Delta V$ and made to enter a region of uniform constant magnetic field $\vec B$. The velocity of the electron and proton are perpendicular to the direction of $\vec B$. Each particle begins to move in a circular arc.

The radius of the electron arc is $r_e$ and that of the proton is $r_p$. Given that the ratio of the electron mass to the proton mass is $\cfrac {m_e}{m_p} = 1837$ determine the ratio of the electron to proton radius $\cfrac {r_e}{r_p}$.

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