One electron has a mass of 9.1 x 10-31 kg. How many coulombs...

Question

One electron has a mass of 9.1 x 10-31 kg. How many coulombs of charge would there be in 1 kg of electrons? How much force would this charge exert on another 1 kg of electrons 1.0 km away? (This is strictly an imaginary situation.) Answers: 1.8 x 1011 C, 2.8 x 1026 N

Answer 1

1 electron has a mass of 9.1 X 10^-31 kg. How many electrons n does it take to make 1 kg?

 

(1 e)/(9.1 X 10^-31 kg) = n/(1 kg)

 

So, n = 1.10 X 10³⁰ electrons

 

Each electron has a charge of 1.6 X 10^-19 C, where C stands for Coulombs. So, the n electrons have a charge of q = ne = (1.10 X 10³⁰ electrons) X (1.6 X 10^-19 C/electron) = 1.76 X 10¹¹ C. This is an insane charge!

 

The electrostatic force between two of these 1kg bundles of electrons is given by Coulomb's law:

 

F = k qq/r² = (8.99 X 10⁹)(1.76 X 10¹¹ C)²/(1000 m)² = 2.78 X 10²⁶ N.