Question

A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge 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 charge particle:

पर्याय

• 1:1

• 1:2

• 2:1

• 1:4

Answer 1

2:1

Explanation:

In a cyclotron, charge is rotated along circular path by magnetic field and it’s kinetic energy is increased by electric field.

Radius of charged particle on circular path is given by

R = `"mv"/"Bq"`

Let the initial speed of charged particle be v Due to application of electric field, it’s kinetic energy increases to 4 times. Thus, new speed of charged particle

4K = `1/2`m(v)²

`"v"^2/("v'")^2 = 1/4`

⇒`"v"/("v'") = 1/2`

⇒ v = 2v

Thus, speed of charged particle becomes doubled.

Let initial radius of circular path be R1 and final radius of circular path be R₂. Then,

R₁ = `"mv"/"Bq"`       ...(1)

R₂ = `("m"xx 2"v")/"Bq"`     ...(2)

from (1) and (2)

R₂ = 2R₁

Thus, Radius gets doubled.