Question

A charged particle is moving in a uniform magnetic field in a circular path of radius R. When the energy of the particle becomes three times the original, the new radius will be ______.

विकल्प

• R

• √3 R

• 3R

• `"R"/3`

Answer 1

A charged particle is moving in a uniform magnetic field in a circular path of radius R. When the energy of the particle becomes three times the original, the new radius will be `underline(sqrt3 "R")`.

Explanation:

The radius of a circular route when a charged particle moves in a uniform magnetic field,

`"R"="mv"/"Bq"`    ....(i)

As momentum p = mv   ...(ii)

and kinetic energy, `"K"=1/2"mv"^2="p"^2/(2"m")`

`=> "p"=sqrt(2"mK")`  ...(iii)

From Eqs. (i), (ii) and (iii), we get

`"R"="p"/"Bq"=sqrt(2"mK")/"Bq"  "or"  "R" propsqrt"K"`

`therefore "R"^'/"R"=sqrt"K"^'/sqrt"K"=sqrt(3"K")/sqrt"K"=sqrt3`       `(because "K"^'=3"K")`

Or  `"R"^'=sqrt3"R"`