Question

A beam of protons (mass 1.67x10^-27kg, charge 1.6x10^-19 coulomb) moves in a circle of radius 25cm. The circle is at right angles to magnetic field 0.3 Tesla. What is the velocity of the protons, the energy of each in Joule and in eV, and what is the time for one to go through one orbit?

Answer 1

The magnetic force on the proton provides centripetal force then

Bqv = mv^2/r

v = rBq/m = 0.25 m ( 0.3 T) ( 1.6* 10 ^-19 C)/ 1.67 * 10 ^-27 kg = 7.18 * 10 ^6 m/s

energy of photon is

KE = (1/2) mv^2

     = (1/2) m(rBq/m)^2

    = (1/2) 1.67 * 10 ^-27 kg (7.18 * 10 ^6 m/s)^2 = 43.0* 10^-15 J( eV/1.6 * 10 ^-19 J) = 26.9 * 10 ^4 eV

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T = 2 pi r/v = 2pi(0.25 m)/7.18 * 10 ^6 m/s = 0.218 * 10 ^-6 s