Cyclotron

Cyclotron

$$ \large F = q v B = \frac{m v^2}{r} $$$$ \large v = \frac{2 \pi r}{T}, \quad \omega = \frac{2 \pi}{T} $$$$ \large v = \frac{q B r}{m} = \frac{2\pi r}{T} $$$$ \large \Rightarrow \quad r = \frac{mv}{qB} $$$$ \large \Rightarrow \quad T = 2 \pi \frac{m}{qB} = \frac{2\pi}{\omega} $$$$ \large \Rightarrow \quad \omega = \frac{qB}{m} $$
  • GRE Physics GR0177: Problem 062

Net Deflected Case

$$ \large qvB = qE $$
  • GRE Physics GR1777: Problem 076

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