A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is:

Question

A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is: (A) (2π mq/B) (B) (2π q2B/m) (C) (2π qB/m) (D) (2π m/qB)

Tardigrade Admin · Accepted Answer

Magnetic force F =q vB ...(i) Centripetal force F=(mv2/r) ...(ii) From Eqs. (i) and (ii). (mv2/r)=qvB r=(mv/qB) The time taken by the particle to complete one revolution, T=(2π r/v) =(2π mv/vqB) =(2 π m/qB)

Q. A charged particle of mass $m$ and charge $q$ travels on a circular path of radius $r$ that is perpendicular to a magnetic field $B$ . The time taken by the particle to complete one revolution is:

$\frac{2 πm q}{B}$

$\frac{2 π q ^{2} B}{m}$

$\frac{2 π qB}{m}$

$\frac{2 πm}{qB}$

Magnetic force $F = q v B ... (i)$
Centripetal force
$F = \frac{m v ^{2}}{r} ... (ii)$
From Eqs. $(i)$ and $(ii) .$
$\frac{m v ^{2}}{r} = q v B$
$r = \frac{m v}{qB}$
The time taken by the particle to complete one revolution,
$T = \frac{2 π r}{v}$
$= \frac{2 π m v}{v qB}$
$= \frac{2 πm}{qB}$

Q. A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is:

B2πmq​

m2πq2B​

m2πqB​

qB2πm​