Question

Four identical metallic spheres with charges of +8.2 µC, +9.0 µC, −7.8 µC, and −8.8 µC are placed on a piece of paper. The paper is lifted on all corners so that the spheres come into contact with each other simultaneously. The paper is then flattened so that the metallic spheres become separated.
a. What is the resulting charge on each sphere?
b. How many excess or absent electrons (depending on the sign of your answer to part (a)) correspond to the resulting charge on each sphere?

Answer 1

Answer:

a) 0.15 μC b) 9.4*10¹¹ electrons.

Explanation:

As the total charge must be conserved, the total charge on the spheres, after being brought to contact each other, and then separated, must be equal to the total charge present in the spheres prior to be put in contact:

Q = +8.2μC +9.0 μC +(-7.8 μC) + (-8.8 μC) = +0.6 μC

As the spheres are assumed perfect conductors, as they are identical, once in contact each other, the excess charge spreads evenly on each sphere, so the final charge, on each of them, is just the fourth part of the total charge:

Qs = Qt/4 = 0.6 μC / 4 = 0.15 μC.

b) As the charge has a positive sign, this means that each sphere has a defect of electrons.

In order to know how many electrons are absent in each sphere, we can divide the total charge by the charge of one electron, which is the elementary charge e, as follows:

$N =\frac{0.15e-6C}{1.6e-19C} = 9.4e11 electrons$