Verified answer

Given σ = -5.0x10^ -3 C/m^2

as 1mm = 10^-3 m

=>σ = -5.0x10^ -3 C/(10^-3mm)^2

=>σ = -5.0x10^3 C/mm^2

=>excess charge per mm^2 (q) = -5.0x10^3 C

by q = ne

=>-5.0x10^3 = n x (-1.6 x 10^-19)

=>n = 3.13 x 10^22

1 mm^2 is 10^-9 m^2.

So excess charge in the given area is 5*10^-3 * 10^-9 = 5*10^-12

hence, the excess electrons are = 5*10^-12 / 1.6 *10^-19 = 3.13*10^7

Electrons have a negative charge of approximately 1.6*10^-19 C, so you simply divide the charge of the balloon by the charge of an electron to find the amount of excess electrons. The unit 'µC' is a micro Coulomb, which means 10^-6 Coulombs. (3.5*10^-6 C)/(1.6*10^-19 C) = 2.1875 * 10^13 electrons