Numerical

A cyclotron's oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons? If the radius of its 'dees' is 60 cm, calculate the kinetic energy (in MeV) of the proton beam produced by the accelerator.

Advertisement Remove all ads

#### Solution

Frequency of oscillators (v) = 10 MH_{z }= 10_{7} H_{z}

Mass of proton, `"m" = 1.67 xx 10^-27 "kg"`

Charge of proton = 1.6 x 10^{-19} C

Operating magnetic field is given by the relation

`"B" = (2pi"mv")/q = (2 xx 3.14 xx 1.67 xx 10^-27 xx 10^7)/(1.6 xx 10^-19)`

= 0.65 T

Radius of dees= 60 cm = 0.6 m

`"KE" = ("q"^2"B"^2"r"^2)/(2"m") = ((1.6 xx 10^-19)^2(0.65)^2(0.6)^2)/(2 xx 1.67 xx 10^-27 xx 1.6 xx 10^-13) "Mev"`.

Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads