A proton X is projected in a region of uniform electric field E with speed u. Another proton Y is projected simultaneously with same speed u in a separate region having a uniform magnetic field ‘B’. It was found that both X and Y had same de-Broglie wavelength after time T. Specific charge on a proton is `sigma (C//kg)`.
(a) Find the angle a at which the proton X was projected with respect to the direction of electric field.
(b) Find the displacement of the proton X in time T.

Answer

(a) `(pi)/(2) + sin^(-1) ((sigmaET)/(2u))` , (b) `sqrt(u^(2) - (sigma^(2)E^(2)T^(2))/(4)) .T`