Question

A particle of mass ' $m$ ' and charge ' $Q$ ' is accelerated in cyclotron. If magnetic field is '$B$' and radius of cyclotron is $r$ then find the kinetic energy of the particle.

• A. $\frac{ QBr }{2 m }$
• B. $\frac{ Q ^{2} B ^{2} r }{2 m }$
• C. $\frac{Q^{2} B^{2} r^{2}}{2 m}$
• D. $\frac{Q^{2} B^{2} r^{2}}{m}$

Answer 1

Answer: (C)

$R =\frac{ mu }{ qB }$
$KE =\frac{1}{2} mu ^{2}=\frac{ Q ^{2} \,B ^{2} \,r^{2}}{2 m }$