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The deflecting plats in a thomas's setup...

The deflecting plats in a thomas's setup are `x` meters long . Intensity of electric field applied between the plates is `E`. The plates are maintained at a `p.d` of `V` volts electrons accelerated through a `p.d V` volts enter from one edge of the plates midway in a direction parellel to the plates . Find the deflection at the other edge of the plates.

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Motion of a charge particle projected perpendicular to a uniform field is a parabola. Horizontal distance travelled by the electron in time ` t "is" X= vtRightarrow t = x/v`
Deflection of the electron in `y-` direction is `y=1/2at^2`,
`F=ma= Ee,a = (Ee)/m , y=1/2((Ee)/m)x^(2)/v^(2)`
`("Since" u_(y)=0) Rightarrowy= (Ee)/(4xx(1/2mv^(2)))x^(2)` ....(1)
We know that, `(1)/(2) mv^(2) = eV` ..(2)
From (1) and (2) `rArr y = (E)/(4V) x^(2)`
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