13. A water droplet of radius 0.018mm remains stationary in air. If the downward electric field in 150N/C, how many excess electrons must the droplet have?
If a droplet remains stationary, net force on it must be zero. There is a force of gravity acting on the droplet,
Fg=mg, where g=9.81 m/s2--acceleration due to gravity, m is the mass of the droplet. It can be found by the formula:
m=ρV; here V is the volume of the droplet, ρ=1000 kg/m3 is the density of water. Volume of a droplet is the volume of a sphere of radius R=0.018mm=1.8*10-5 m. V=4/3πR3; Final formula for the force of gravity is as follows:
The force, which opposes it, is the electrical force, Fe. It can be found as Fe=Eq, where E is the electric field, q is the charge. Overall charge equals the charge of one electron, e, (e=1.6*10-19 C) times the number or excess electrons, N. So, electric force is:
Two forces must be equal, thus giving:
From this we obtain:
After some calculations, we obtain: