Problem 3.379

A charged particle moves along a circle of radius \(r=100 \mathrm{~mm}\) in a uniform magnetic field with induction \(B=10.0 \mathrm{mT} .\) Find its velocity and period of revolution if that particle is (a) a non-relativistic proton; (b) a relativistic electron.

Reveal Answer

\begin{aligned} &\text { (b) } v=\\ &\begin{aligned} & \text { 3.379. (a) } v=r e B / m=100 \mathrm{~km} / \mathrm{s}, T=2 \pi m / e B=6.5 \mu \mathrm{s} ; \\ =& c / \sqrt{1+\left(m_{0} c / r e B\right)^{2}}=0.51 c, \quad T=\frac{2 \pi m_{0}}{e B \sqrt{1-\left(v / c^{2}\right)}}=4.1 \mathrm{~ns} \end{aligned} \end{aligned}

Motion of Charged Particles in Electric and Magnetic Fields