The cyclotron frequency upsilonc is given by

Question

The cyclotron frequency upsilonc is given by (A) (qB/2 π m) (B) (mB/2π q) (C) (2π m/qB) (D) (2π B/qm)

Tardigrade Admin · Accepted Answer

In cyclotron the centripetal force is balanced by magnetic force, then qvB=(mv2/r) ⇒ (qBr/m)=v where v=2π r upsilonc (qBr/m)=2π r upsilonc ∴ upsilonc=(qB/2 π m)

Q. The cyclotron frequency $υ_{c}$ is given by

$\frac{qB}{2 πm}$

$\frac{m B}{2 π q}$

$\frac{2 πm}{qB}$

$\frac{2 π B}{q m}$

In cyclotron the centripetal force is balanced by magnetic force, then
$q v B = \frac{m v ^{2}}{r}$
$\Rightarrow \frac{qB r}{m} = v$
where $v = 2 π r υ_{c}$
$\frac{qB r}{m} = 2 π r υ_{c}$
$∴ υ_{c} = \frac{qB}{2 πm}$

Q. The cyclotron frequency υc​ is given by

2πmqB​

2πqmB​

qB2πm​

qm2πB​