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In a region of space, a uniform magnetic...

In a region of space, a uniform magnetic field `B` is along positive x-axis. Electrons are ernit.u.d from the origin with speed `u` at different, angles. Show that the paraxial electrons are refocused on the x-axis at a distance `(2pimv)/(Be)`. Here, `m` is the mass of electron and e the charge on it.

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Verified by Experts

The correct Answer is:
A

Electrons touch the x-axis again after every pitch.
Therefore the asked distasnce is
`d=p=v_11T=(vcsotheta)((2pim)/(Bq))`
For paraxial electron `theta=0^@ and q=e`,
`:. D=(2pimv)/(B3)`
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