CBSE Class 12 · 2009 · All India · Magnetic Effects of CurrentLong Answer

\textbf{Working:} inside the two dees a magnetic field bends the ion into semicircles; each time it crosses the gap the alternating electric field accelerates it, so its radius grows while it gains energy. (i) $qvB=\frac{m{v}^2}{r}\Rightarrow r=\frac{mv}{qB}$, so with no $v$ or $r$ — the period is fixed. (ii) \textbf{Resonance condition:} the applied frequency equals the cyclotron frequency $f=\frac{qB}{2\pi m}$. Then the field reverses exactly as the ion reaches the gap each half-turn, giving it a push every crossing and steadily increasing its energy.