Question

Two spherical objects are separated by a distance of 1.06 × 10^-3 m. The objects are initially electrically neutral and are very small compared to the distance between them. Each object acquires the same negative charge due to the addition of electrons. As a result, each object experiences an electrostatic force that has a magnitude of 10.0 × 10^-21 N. How many electrons did it take to produce the charge on one of the objects?

Answer 1

The electric force between the objects can be expressed as:

F_e = kq²/r² where
k is electrostatic constant 9*10⁹ N.m²/C²
q is the charge of each object
r is the distance separating them

So
q = (Fe.r²/k)^0.5
q = (10*10^-21*(1.06*10^-3)²/9*10⁹)^0.5

=1.117*10^-18 (with minus sign since it is negative)

One electron has charge
e = 1.6*10^-19 C

So this charge represents q/e electrons
q/e = 1.117*10^-18/1.6*10^-19

= 7 electrons