a. In a planar capacitor of length l, the electric field strength is equal to E, and the magnetic field induction directed along E is equal to B. At the entrance to the capacitor, there is a radioactive source that emits electrons at different speeds. From them, a thin beam is formed, which passes through a capacitor, and then falls on a photographic plate located at a distance of L ≫ l. What trace line will the electrons "draw" on the photographic plate, if their deviations from the rectilinear trajectory are small?
b. Find the line-trace of electrons on the photographic plate for B = 1 T, E = 5⋅105 V/m, l = 5 cm, L = 50 cm.
c. At high electron velocity, its mass changes noticeably; according to the Lorentz formula, m = 1−β2me, where β is the ratio of the electron velocity to the speed of light, and me is the rest mass of the electron. Solve the problem 10.1.17a taking into account the effect of changing the mass of the electron.