First slide

Force on a charged particle moving in a magnetic field

Question

Maximum kinetic energy of the positive ion in the cyclotron is ( $r_{0} = R a d i u s o f c y c l o t r o n, q = c h a r g e o f i o n, m = m a s s o f i o n)$

Moderate

A

$\frac{q^{2} {Br}_{0}}{2 m}$
B

$\frac{q B^{2} r_{0}}{2 m}$
C

$\frac{q^{2} B^{2} r_{0}^{2}}{2 m}$
D

$\frac{{qBr}_{0}^{}}{2 m^{2}}$

Solution

$\begin{array}{l} K_{\max} = \frac{1}{2} {mv}^{2} and r_{0} = \frac{mv}{qB} \Rightarrow v = \frac{{qBr}_{0}}{m} \\ K_{\max} = \frac{1}{2} m {(\frac{{qBr}_{0}}{m})}^{2} = \frac{q^{2} B^{2} r_{0}^{2}}{2 m} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App