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A Cyclotron is Used to Accelerate Protons to a Kinetic Energy of 5 Mev. If the Strength of Magnetic Field in the Cyclotron is 2t, Find the Radius and the Frequency Needed for the Applied Alternating - Physics

A cyclotron is used to accelerate protons to a kinetic energy of 5 MeV. If the strength of magnetic field in the cyclotron is 2T, find the radius and the frequency needed for the applied alternating voltage of the cyclotron. (Given : Velocity of proton= `3xx10^7 m//s`)

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Solution

`K.E = 5Me V `

`B= 2T`

`r= ?`

`f=?`

`v=3xx10^7m//s`

`r= (mv)/(Bq)=(1.67xx10^-27 xx3xx10^7)/(2xx1.6xx10^-19)=0.1565 m`

`f=(qB)/(2pim)= (1.6xx10^-19xx2)/(2xx3.14xx1.67xx10^-27)= 3.05 xx 10^7 Hz`

Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron
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