BITSAT 2024 Shift 1 Paper

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=4×10−12‌mg
Conversion to kilograms:
m=4×10−12×10−3g=4×10−12×10−3×10−3‌kg=4×10−18‌kg
Electric field strength, E=50N∕C
Gravitational acceleration, g=10m∕ s2
Calculate the Weight:
The weight W of the dust particle is given by:
W=m×g=4×10−18×10=4×10−17N
Equating Electric Force to Weight:
The electric force Fe experienced by the dust particle is:
Fe=q×E
Where 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=W
‌n×1.6×10−19×50=4×10−17
Solving for n :
n=‌

4×10−17

1.6×10−19×50

n=‌

400

80

=5
Therefore, 5 electrons were removed from the neutral dust particle.