Q: The deflecting plates in Thomson’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 of V

volts enter from one edge of the plated midway in a direction parallel to the plates. Find the deflection

at the other edge of the plates.

Sol: Motion of a charged particle projected perpendicular to a uniform electric field is a parabola. Horizontal

distance travelled by the electron in times t is

$\large x = v t \Rightarrow t = \frac{x}{v} $

Deflection of the electron in y – direction is

$\large y = 0 + \frac{1}{2} a t^2 $

$\large y = \frac{1}{2} (\frac{e E}{m}) (\frac{x}{v})^2 $

(since u_{y} = 0)

$\large y = \frac{1}{4} (\frac{e E}{\frac{1}{2}m v^2})x^2 $ …(i)

We known that, $\large \frac{1}{2} m v^2 = e V $ …….(ii)

From (i) and (ii)

$\large y = \frac{E}{4 V} x^2 $