A monoenergetic `(18keV)` electron beam initially in the horizontal direction is subjected to a horizontal magnetic field of `0*40G` normal to the initial direction. Estimate the up or down deflection of the beam over a distance of `30cm`. Given mass of electron `9.11xx10^(-31)kg` and charge on electron `=1*6xx10^(-19)C`. [Note. Data in this exercise are so chosen that the answer will give you an idea of the effect of earth's magnetic field on the motion of electron beam from electron gun to the screen in a T.V. set].

Explanation

Here, energy `E=18keV=18xx1*6xx10^(-16)J`, `B=0*40G=0*40xx10^-4T`, `x=30cm=0*3m`
As, `E=1/2mv^2` `:. v=sqrt(2E//m)`
In a magnetic field, electron beam is deflected along a circular arc of radius r, such that
`Bev=(mv^2)/(r)` or `r=(mv)/(Be)`
`r=(m)/(Be)sqrt((2E)/(m))=(1)/(Be)sqrt(2Em)=11.3m`
If y is the deflection at the end of the path, then as is clear from figure.
`theta=x/r=(y)/(x//2)=2y/x`
or `y=(x^2)/(2r)=(0.30xx0.30)/(2xx11.3)m=0.004m=4mm`