First slide

Force on a charged particle moving in a magnetic field

Question

Statement 1: A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal.
Statement 2: Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field $\vec{B}$ in a direction perpendicular to $\vec{B}$ , will describe circular trajectories of equal radii.

Moderate

A

Both statements 1 and 2 are correct
B

Statement 1 is correct statement 2 is incorrect
C

Statement 1 is incorrect statement 2 is correct
D

Both statements 1 and 2 are incorrect

Solution

The radius of the circular path is given by
$r = \frac{mv}{qB} = \frac{\sqrt{2 mK}}{qB}; where K = \frac{1}{2} {mv}^{2}$
Since K and B are the same for the two particles, $r \propto \frac{\sqrt{m}}{q} .$ Now, the charge of an alpha particle is twice that of a proton and its mass is four times the mass of a proton, $\sqrt{m} / q$ will be the same for body particles. Hence, r will be the same for both particles.

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