All Problems

Motion of Charged Particles in Electric and Magnetic Fields

Problem 3.407

The magnetic induction in a betatron on an equilibrium orbit of radius rr varies during the acceleration time at practically constant rate from zero to BB. Assuming the initial velocity of the electron to be equal to zero, find: (a) the energy acquired by the electron during the acceleration time; (b) the corresponding distance covered by the electron if the acceleration time is equal to Δt\Delta t

Reveal Answer
(a) W=(1+(reB/m0c)2−1)m0c2W=\left(\sqrt{1+\left(r e B / m_{0} c\right)^{2}}-1\right) m_{0} c^{2} (b) s=WΔt/reBs=W \Delta t / r e B.
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