All Problems

Motion of Charged Particles in Electric and Magnetic Fields

Problem 3.402

In a betatron the magnetic flux across an equilibrium orbit of radius \(r=25 \mathrm{~cm}\) grows during the acceleration time at practically constant rate \(\dot{\Phi}=5.0 \mathrm{~Wb} / \mathrm{s} .\) In the process, the electrons acquire an energy \(W=25 \mathrm{MeV} .\) Find the number of revolutions made by the electron during the acceleration time and the corresponding distance covered by it.

Reveal Answer
N=W/eΦ˙=5⋅106 revolutions, s=2πrN=8⋅103 kmN=W / e \dot{\Phi}=5 \cdot 10^{6} \text { revolutions, } s=2 \pi r N=8 \cdot 10^{3} \mathrm{~km}
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