Problem 34.31 (RHK)
A 22.5-eV positron (positively charged electron) is projected into a uniform magnetic field with its velocity vector making an angle of with . We have to find (a) the period, (b) the pitch p, and (c) the radius r of the helical path.
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It is given that the velocity vector makes an angle of with the magnetic field vector . Magnitude of the magnetic field vector
We will first find the magnitude of velocity of a 22.5-eV positron.
We resolve the velocity vector into components, , which is parallel to the field, and ,which is orthogonal to the magnetic field vector .
The radius of the helical path will be determined by and the pitch by .
The period of the circular orbit is therefore
The pitch of the helical path
The radius of the helical path