A beam of electrons moving with a velocity Of 101 m/s enters midway between two horizontal parallel plates which
Que 5cm long. 2cm apart and have pod Of V volt
applied between them - Calculate v if the beam is deflected
so that it just grazes the edge of the lower plate.(e/m = 1.8×10^11 c/kg)

Explanation:

electrical field in vertical direction = V / .02  , .02 is distance between plate and V is potential difference .

force on electrons = V x e / .02

acceleration of falling electrons

= V x e /( .02  x m )

= 50 x 1.8 x 10¹¹ V

a = 9 x 10¹² V .

Time to cover length of plate

t = .05 / 10⁷ = 5  x 10⁻⁹ s ,      velocity of electron = 10⁷ m /s .

vertical distance covered by electron s = .01 m with acceleration a in time t

s = 1/2 a t²

.01 = .5 x 9  V  x 10¹²  x ( 5 x 10⁻⁹ )²

10⁻² = 4.5 x 25  x 10⁻¹⁸ x 10¹² V

V = 10⁴ /  (4.5 x 25)

= 88.89 Volt .

v=ir = 3x15 =45 v