All Problems Motion of Charged Particles in Electric and Magnetic Fields
Problem 3.377
At the moment \(t=0\) a relativistic proton flies with a velocity \(\mathbf{v}_ {0}\) into the region where there is a uniform transverse electric field of strength \(\mathrm{E}\), with \(\mathbf{v}_ {0} \perp \mathbf{E}\). Find the time dependence of (a) the angle \(\theta\) between the proton's velocity vector \(\mathbf{v}\) and the initial direction of its motion; (b) the projection \(v_{x}\) of the vector \(\mathbf{v}\) on the initial direction of motion.
3.377. (a) \(\tan \theta=\frac{e E t}{m_{0} v_{0}} \sqrt{1-\left(v_{0} / c\right)^{2}}\), where \(e\) and \(m_{0}\) are the charge and the mass of a proton; (b) \(v_{x}=v_{0} / \sqrt{1+\left(1-v_{0}^{2} / c^{2}\right)\left(e E t / m_{0} c^{2}\right)^{2}}\)