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.

Answer

51mm.

Explanation

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.