An electron entering an extended stationary and uniform electric field at the velocity βc departs from it after a time τ The electron velocity is directed along the field. How long will an electron stay in the field if, on the contrary, the field hits a stationary electron with the same speed? Solve this problem in two ways, using: a) relativistic deceleration effect of time, b) the Lorentz formula, according to which the mass of a particle moving at a speed of βc, m = 1−β2mi, where mi is the rest mass of the particle.
*) If the problem does not require a numerical answer, denote the rest mass of the electron me, the charge e.