Two particles of masses \(m_1\) and \(m_2\) having charges \(q_1\) and \(q_2\) respectively are projected with the same velocity in a region of uniform magnetic field \(\vec{B}\) pointing vertically upward. If they describe circular paths as shown in the figure, one may conclude that :
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When tracking particles in magnetic field problems, always remember that the radius of a circular trajectory is directly proportional to the mass-to-charge ratio (\(m/q\)) when the velocity \(v\) and field \(B\) are held constant:
\[
R \propto \frac{m}{q}
\]
A smaller radius directly implies a smaller value of \(\frac{m}{q}\). Therefore, seeing that curve 1 is tighter (\(R_1 < R_2\)), you can immediately write \(\frac{m_1}{q_1} < \frac{m_2}{q_2}\) and cross-multiply to reach the final answer in seconds.
