Question

In a certain cyclotron a proton moves in a circle of radius 0.730 m. The magnitude of the magnetic field is 1.20 T. (a) What is the oscillator frequency? (b) What is the kinetic energy of the proton?

Answer 1

Given,

Charge of proton, q= 1.6 x10^-19 C

Magnetic field, B = 1.20 T

Mass of proton, m = 1.67 x 10^-27 kg

Radius, r = 0.730 m

A)

Frequency, f = qB/ 2 pi m =

F = (1.6 x10^-19) 1.2 / ( 2 x 3.14 x (1.67 x 10^-27) )

= 1.83 x 10^7 Hz

B)

Kinetic energy, KE = 0.5 mv^2 = 0.5 x m x (qBr/m)^2

= 0.5(qBr)^2 / m

= 0.5 x ((1.6 x 10^-19) x 1.2 x 0.73)^2/ (1.67 x 10^-27)

= 5.88 x 10^-12 J (1 eV / 1.602 x 10^-19)

= 3.68 x 10^7 eV

Comment in case any doubt please rate my answer ... .