Question

A metal cube measuring one inch on a side has taken on a charge of 0.1 Coulombs. On average, how many extra electrons are there in each cubic centimeter of metal?   Would you expect the distribution of electrons in the metal cube to be uniform? Why?

Answer 1

From the relation

Q= ne

Where n = number of electron

e = electronic charge

Q = total charge

n=Q/e

n = 0.1/1.6×10^-19

n = 6.25×10¹⁷ electrons.

This is total extra electron on the cube in 2.54³ cm^{​​​​​3}​

1 inch = 2.54 cm

In 1 cm^{​​​​​3}​ number of electron=

Number of electron = 3.8×10¹⁶ electrons

Yes, the distribution will be uniform because cube is a symmetric object and symmetric objects have uniform distribution. Further it is a metal cube thus the electron can reside in whole volume.