Question

A charged particle is projected in a plane perpendicular to uniform magnetic field. The areal velocity (area swept per unit time) of the particle is :

• A. directly proportional to kinetic energy of particle
• B. directly proportional to momentum of the particle
• C. inversely proportional to magnetic field strength
• D. inversely proportional to charge on particle

Answer 1

Answer: (A), (B), (C), (D)

$F=qvB$

$r=\frac{mv}{qB}$

areal velocity$=\frac{\pi r^2}{T}$

$=\pi {\left(\frac{mv}{qB}\right)}^2\times \frac{qB}{2\pi m}$

$=\frac{m{v}^2}{2qB}$