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The electron beam in the device shown in...

The electron beam in the device shown in Fig. 28.7a is deflected upwards by a transverse magnetic field. The field is effective along a length l= 20 mm, the distance of the deflection system from the screen being L =175 mm. The magnetic induction is `10^(-3)T,` the anode voltage is 500 V. Find the deflection of the electron beam on the screen.

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The correct Answer is:
51mm.
The electrons in this problem are nonrelativistic, they enter the magnetic field at a speed `u=sqrt(2e Psi//m)=1.33 xx 10^(7) m//s`. In the magnetic field they move along an arc of a circle of radius `R=um//eB` (Fig 28.7b). The electrons are deflected through an anle `angleGCE=alpha`. But the angle `angleGCE` is congruent to the angle `angleCOM` (as angles with mutually perpendicular sides). Therefore `sin alpha=(MC)/(OC)=l/R=(e Bl)/(m_(e)u)=(e Bl)/sqrt(2m_(e)e Psi)`
As is evident from the figure, GD=GE+EB, or
`d=L tan alpha +R (1-cos alpha)=L tan alpha+l (1-cos alpha)/(sin alpha)=L tan alpha+l tan ""pi/2`
Knowing the parameters of the device one may easily calculate the displacement sought.
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