Question

a capacitor is built by separating two 20cm by 20cm square copper plates 1.2mm from one another. the pair of plates is then connected to a 2400V power supply. between the plates you will inject a small droplet of oil (rho = 900kg/cm3) which has been exposed to a Cs-137 source, which caused it to be 300 times ionized. if the E field points upward, what is the maximum radius of oil droplet you could inject to stay suspended in midair with this power supply?

Answer 1

V 2400 d 1.2 x 10-3N/C

E = 2 x 106/

Charge on the droplet

q=qe x 300 = 480 x 10-19C = 4.8 x 10-110

Electrostatic force on the droplet is

F=qE

F= 2 x 106 x 4.8 x 10-1) = 9.6 x 10-11

for the droplet to be at rest its weight should be equal in magnitude to the force excerted by the electric field.

mg = F

p(4113)g = F

F 411pg

2 т= 9.6 х 10-11 \ 4П x 900 x 108 х 9.8) ( 4 x 10-19 Пх3x 49,

T= 0.4424 x 10-meters

r=0.4424um