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An electron accelerated in an electric field of 20 kV enters a uniform magnetic field with induction 0.1 T. Its velocity vector makes an angle of 75^@ with the magnetic field vector. Find the shape of the path.

Answer»


Solution :In the field the electron acquires a kinetic energy of 20 kev, which is much less than its rest energy (511 KCV). Therefore in this problem it is a nonrelativistic particle. Resolve the electron velocity into two comportents: one along the line of induction,and the other perpendicular to it, `v_(bot) =v sin a` (Fig. 28.5). No forces act on the electron in the longitudinal direction, therefore the electron will move at a constant speed along the z-axis according to the equation. `z_(0)+vt cos ALPHA`
In the lateral direction (i.e. in the my plane) the electron is acted upon by the Lorentz force, which makes the PROJECTION of its motion in this plane a circle with radius `R=(mv_(bot))/(e B)=sqrt(2me_(Psi) sin alpha)/(e B)`
and with PERIOD `T 2pim//eB` In space the election moves along a helix which winds around the lines of induction. The radius of the circle, R, was given above. The pitch of the helix is `h=v_(1) T (2pi mv cos alpha)/(e B)-2pi R cot alpha`.


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