Question

3 Charge Deflector An experiment to look for a charge imbalance between the proton and electron is constructed as shown. A beam of particles moving at speed vo 1.0 106 m/s is prepared in an accelerator. Before striking the detector, the beam passes through a 10 m region that contains a uniform elec- tric field of 100 N/C perpendicular to the beam. (a) Where would a proton from the beam be expected to strike the detector? (Le., how many meters above or below the beam line would it strike?) beam (b) Suppose the experiment is unable to detect a deflec- tion less than 1 nm. If no deflection of hydrogen atoms is detected (i.e., the deflection of a hydrogen atom is less than 1 nm), what is the upper limit on the net charge of a hydrogen atom? This is the maximum difference between the electron and proton charge that is consistent with the experimental measurement 10 m

Answer 1

(a) Proton charge = 1.6 times 10^-19 C initial velocity (v) = 1.0 times 10^6 m/sec Force due to electric field will not alter the horizontal velocity 'v'. Because this force is perpendicular to velocity. Now time required (t) to reach at the detector = t/v = 10 m/1.0 times 10^6 m/sec = 10^-5 sec Force on the proton = qE = 1.6 times 10^-19 times 100 N = 1.6 times 10^-17 N acceleration of proton = F/m = 1.6 times 10^-17/1.67 times 10^-27 m/sec^2 = 0.95 times 10^10 m/sec^2 Now deviation in vertical direction = 1/2 at^2 = 1/2 times 0.95 times 10^10 times (10^-5)^2 = 0.95/2 m = 0.479 m (b) Similarly deviation = ln m (boundary value) 1/2 a times (10^-5)^2 = 1 times 10^-9 m a = 2 times 10^-9/10^-10 = 20 m/sec^2 a = qE/m = 20 m/sec^2 q = 20 times m/E 20 times 1.6 times 10^-27/100 q = 3.2 times 10^-28 C