Question

In the cyclotron, as radius of the circular path of the charged particle increases ($\omega =$ angular velocity, $v=$ linear velocity)

• A. Both $\omega$ and $v$ increases
• B. $\omega$ only increases, $v$ remains constant
• C. $v$ increases, $\omega$ remains constant
• D. $v$ increases, $\omega$ decreases

Answer 1

Answer: (C)

$v$ increases, $\omega$ remains constant

Linear velocity, $v=\frac{Bqr}{m}$

$⟹$ $v\propto r$

Also angular velocity, $w=\frac{Bq}{m}$

$⟹$ $w=constant$ $(\because B,q,m$ are constants$)$

Hence, $v$ increases whereas $w$ remains constant when the radius of circular path is increased.