All Problems

Motion of Charged Particles in Electric and Magnetic Fields

Problem 3.400

The ill effects associated with the variation of the period of revolution of the particle in a cyclotron due to the increase of its energy are eliminated by slow monitoring (modulating) the frequency of accelerating field. According to what law ω(t)\omega(t) should this frequency be monitored if the magnetic induction is equal to BB and the particle acquires an energy ΔW\Delta W per revolution? The charge of the particle is qq and its mass is mm.

Reveal Answer
ω=ω0/V1+at‾, where ω0=qB/m,a=qBΔW/πm2c2\omega=\omega_{0} / V \overline{1+a t}, \text { where } \omega_{0}=q B / m, a=q B \Delta W / \pi m^{2} c^{2}
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