A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle :

Question

A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle : (A) 1: 1 (B) 1: 2 (C) 2:1 (D) 1: 4

Tardigrade Admin · Accepted Answer

radius of paerticle in cyclotron r=(√2 mK ⋅ E ./ qB ) So ratio of new radius to original (rn/r0)=√(( text K.E. )n/( text K.E )0) =√4 ⇒ 2: 1

Q. A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to $4$ times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle :

$1 : 1$

$1 : 2$

$2 : 1$

$1 : 4$

radius of paerticle in cyclotron
$r = \frac{2 m K \cdot E .}{qB}$
So ratio of new radius to original
$\frac{r _{n}}{r _{0}} = \frac{( K.E. ) _{n}}{( K.E ) _{0}}$
$= 4 \Rightarrow 2 : 1$

Q. A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle :

1:1

1:2

2:1

1:4