A beam of particles with velocity (v, 0,0) enters a region containing crossed el

Question

A beam of particles with velocity (v, 0,0) enters a region containing crossed electric and magnetic fields, as in the example at the end of sect5.2. Show that if the ratio E/B is correctly chosen the particles are undeviated, while particles with other speeds follow curved trajectories. Suppose the particles have velocities equal to v in magnitude, but with a small angular dispersion. Show that if the path length I is correctly chosen, all such particles are focused onto a line parallel to the z-axis. (Thus a slit at that point can be used to select particles with a given speed.) For electrons of velocity 10^8 m s^-1 in a magnetic field of 0.02T, find the required electric field, and the correct (smallest possible) choice for I.

Explanation / Answer

Apply,

for no deflection,
q*E = q*v*B

==> E = v*B

= 10^8*0.02

= 2*10^6 N/c <<<-----Answer

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