A spherical water droplet of radius 25 μm carries an excess 250 electrons. CONTINUED IN DESCRIPTION

Question

What magnitude of vertical electric field is needed to balance the gravitational force on the droplet at the surface of the earth? SHOW ALL WORK

Answer 1

Doing a force balance on the drop: F_W = F_E for equilibrium. Weight = Electrical Force

Units are critical!

F_W = mg = ρ(4/3)πR³g = (1000 kg/m³)(4/3)π(25x10^-6 m)³

F_E= QE = 250q_eE = 250(1.6x10^-19 Coul) E

Equate and solve for E in Volts/meter or Newtons/Coulomb (same units)