To determine how many electrons have been removed from a neutral dust particle suspended in an electric field, let's go through the calculations step by step.
Given:
Mass of the dust particle,
m=4×10−12mgConversion to kilograms:
m=4×10−12×10−3g=4×10−12×10−3×10−3kg=4×10−18kgElectric field strength,
E=50N/CGravitational acceleration,
g=10m/s2Calculate the Weight:
The weight
W of the dust particle is given by:
W=m×g=4×10−18×10=4×10−17NEquating Electric Force to Weight:
The electric force
Fe experienced by the dust particle is:
Fe=q×EWhere
q=n×e, with
e=1.6×10−19 C as the charge of one electron, and
n being the number of electrons removed.
At equilibrium, the electric force equals the weight of the particle:
n×e×E=Wn×1.6×10−19×50=4×10−17Solving for
n :
n=1.6×10−19×504×10−17n=80400=5Therefore, 5 electrons were removed from the neutral dust particle.