Question

(b) Estimate the angular deflection of a beam of atoms after passing through a magnet 0.5 m long which produces a field gradient of 500 T/m in a direction perpendicular to the direction of motion of the atoms. Assume that only one electron in the atom is responsible for its magnetic moment, and that this is an s-electron. The atoms originate in an oven at 1800 K. Point out any approximations you make.

Answer 1

Force in inhormogenious magnetic field on e^- F = -nabla (M.B) = -M nabla.B = -M dB/dz ml theta = + M dB/dz(magnitude) where M rightarrow (mu_e) = magnetic moment of e^- m = mass of the e^- l = length of magnet theta = -(- 9.28 times 10^-24) times 500/9.1 times 10^-31 times 0.5 = 9.284 times 500/9.1 times 0.5 times 10^-24 + 31 = 1020.22 times 10^7 theta = (1.020 times 10^10) sec^- 2 = A (say) theta = At + C = > theta = At^2/2 + Ct + C_1 t = 0, theta = 0 theta = 0 + 0 + C_1 = > C_1 = 0 0 = 0 at t = 0, 0 = A times 0 + C = > C = 0 theta = 1/2 At^2 if e^- takes u see to pass through magnet theta = 1/2 times (1.020 times 10^10) times 10^-12 = 0.510 times 10^-2 = 29.23 degree times 10^-2 theta = 0.29 degree