All Problems

Motion of Charged Particles in Electric and Magnetic Fields

Problem 3.406

In a betatron the magnetic induction on an equilibrium orbit with radius r=20 cmr=20 \mathrm{~cm} varies during a time interval Δt\Delta t =1.0 ms=1.0 \mathrm{~ms} at practically constant rate from zero to B=0.40 T.B=0.40 \mathrm{~T} . Find the energy acquired by the electron per revolution.

Reveal Answer
ΔW=2πr2eB/Δt=0.10keV\Delta W=2 \pi r^{2} e B / \Delta t=0.10 \mathrm{keV}