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

A helix winding around the lines of induction. The radius of the circle is 23mm, the bitch is 39mm.

Explanation

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`.