3. An oil droplet with a mass of 9.8 x 104 kg travels in a tube between two char

Question

3. An oil droplet with a mass of 9.8 x 104 kg travels in a tube between two charged metal plates with a length of 2.0 cm. These plates generate an electric field with a magnitude of 8.1 x 103 N/C. When the droplet reaches the end of the tube, it has been displaced from its original course by 1.5 x 10-3 cm, and has a speed of 28m/s. a. Find the net charge of the droplet once it has reached the end of the tube (ignore gravity) b. What is the change in potential energy? c. What is the electric potential?

Explanation / Answer

3. (a) suppose initial speed was v then  

time taken to cross t = L / v

and deflection,

d = 0 + a t^2 / 2

d = a (L/v)^2 / 2

1.5 x 10^-3 x 10^-2 = a (0.02/ 2) / v^2

a / v^2 = 1.5 x 10^-3 .... (i )

and vf = a t = a (L/v)

vf = 0.02 a / v

28^2 = (vf^2 + v^2)

28^2 = 0.0004 a^2 / v^2 + v^2

putting v^2 = 666.67 a

28^2 = (0.02)^2 a^2 / (666.67 a) + 666.67a

a = 1.176 m/s^2  

a = q E / m

(9.8 x 10^-4 ) (1.176) = q (8.1 x 10^-3)

q = 0.1423 C .....Ans

(b) change in PE = - q E d = - 0.1423 x 8.1 x 10^-3 x 1.5 x 10^-5

= - 17.3 x 10^-9 J

(C) potential = 2 E d = 0.243 x 10^-6 Volt

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