In the cyclotron, as radius of the circular path of the charged particle increases ω= angular velocity, v= linear velocity

Question

In the cyclotron, as radius of the circular path of the charged particle increases ω= angular velocity, v= linear velocity (A) Both ω and v increase (B) Only ω increases, v remains constant (C) Only v increases, ω remains constant (D) v increases, ω decreases

Tardigrade Admin · Accepted Answer

In a cyclotron R=(m v/q B) v=(q B R/m) and ω =(q B/m) ∴ R propto v. ω ,q,m and B are constant.

Q. In the cyclotron, as radius of the circular path of the charged particle increases
$ω =$ angular velocity, $v =$ linear velocity

Both $ω$ and $v$ increase

Only $ω$ increases, $v$ remains constant

Only $v$ increases, $ω$ remains constant

$v$ increases, $ω$ decreases

In a cyclotron
$R = \frac{m v}{qB}$
$v = \frac{qBR}{m}$ and $ω = \frac{qB}{m}$
$∴ R \propto v .$
$ω, q, m$ and $B$ are constant.

Q. In the cyclotron, as radius of the circular path of the charged particle increases ω= angular velocity, v= linear velocity

Both ω and v increase

Only ω increases, v remains constant

Only v increases, ω remains constant

v increases, ω decreases