First slide

Force on a charged particle moving in a magnetic field

Question

A proton and an $α - particle,$ accelerated through the same potential difference, enter a region of uniform magnetic field normally. If the radius of the proton orbit is 10 cm, then that of $α -$ orbit is

Moderate

Solution

$\begin{array}{l} \frac{1}{2} {mu}^{2} = Q . V \Rightarrow u = \sqrt{\frac{2 QV}{m}}, r = \frac{u}{ω} = \sqrt{\frac{2 QV}{m}} \times \frac{m}{QB} = \frac{1}{B} . \sqrt{\frac{2 Vm}{Q}} \\ ∴ \frac{r_{\propto}}{r_{P}} = \sqrt{\frac{m_{α}}{m_{p}}} . \sqrt{\frac{Q_{P}}{Q_{α}}} = \sqrt{4} . \frac{1}{\sqrt{2}} = \sqrt{2} \Rightarrow r_{\propto} = 10 \sqrt{2} cm \end{array}$

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