Deuterons in a cyclotron describes a circle of radius `32.0cm`. Just before emerging from the `D's`. The frequency of the applied alternating voltage is `10MHz`. Find, `(a)` the magnetic flux density `( i.e.,` the magnetic field `), (b)` the energy and speed of the deuterons upon emergence.

Answer

`4.22MeV`

Explanation

`(a)` Frequency of the applied emf`=` Cyclotron frequency or `f=(Bq)/(2pim),B=(2pimf)/(q)`
`=((2)(3.14)(2xx1.67xx10^(-27))(10xx10^(6)))/(1.6xx10^(-19))=1.30T`
`(b)` The speed of the deutrons on the emergence from the cyclotron,
`v=(BqR)/(m)=2pifR`
`=(2)(3.14)(10xx10^(6))(32xx10^(-2))=2.01xx10^(7)m//s`
`:." "` Energy of deutrons `=(1)/(2)mv^(2)`
`=(1)/(2)xx(2xx1.67xx10^(-27))(2.01xx10^(7))^(2)J`
`4.22MeV`