Problem 12 - Olympiad

The radius of the circular path of a charged particle in a magnetic field can be calculated using the formula r = mv / (qB), where r is the radius, m is the mass of the particle, v is the velocity, q is the charge, and B is the magnetic field strength. Given that the proton and electron have the same charge magnitude but opposite signs and assuming the masses of the proton and electron are approximately 1.67 * 10^-27 kg and 9.11 * 10^-31 kg respectively, we can set up the ratio of their radii as (m_p * v_p) / (q * B) : (m_e * v_e) / (q * B). Simplifying and canceling out q and B from both sides gives us (m_p * v_p) : (m_e * v_e). Substituting the given velocities and the mass values, we get (1.67 * 10^-27 * 2 * 10^6) : (9.11 * 10^-31 * 3 * 10^6), which simplifies to (3.34 * 10^-21) : (2.733 * 10^-24), and simplifying the ratio gives us approximately 1837:1. However, considering the velocities and masses involved and looking for a simplified comparison based on question options provided, the closest and most simplified answer given our calculation approach and based on typical problem solving expectations for these types of questions is not directly listed. Thus, a mistake was made in calculation explanation - correct approach should directly compare the r = mv/(qB) for both, recognizing the mass and velocity relationship would yield a much simpler answer when considering electron to proton mass ratio is about 1:1836, and thus if both were moving at the same speed, the radius ratio would be proportional to their mass ratio, but given the velocity and mass difference and simplifying our previous error, we recognize a direct answer wasn't provided based on calculation oversight. Realistically for a multiple choice and correcting for the simplification and calculation mistake, we'd consider basic principles of magnetic field and charge interaction leading to a simplification error in calculation explanation.