# Coulomb's Law of two copper spheres

1. Jan 21, 2005

### eil2001

Here's a question from my textbook:

Two copper spheres, each having a mass of .4 kg, are separated by 2 m.
(a) How many electrons does each sphere contain? The atomic mass of copper is 63.5 g/mol, and its atomic number is 29.
(b) How many electrons would have to be removed from one sphere and added to the other to cause an attractive force of 1.00x10^4 N (roughly 1 ton)?

I got (a) by dimensional analysis:
(.4 kg Cu) x (1 mol/.0635 kg Cu) x (6.02x10&23 molec/1 mol) x (29 electrons/molec) = 1.10x10^26 electrons

But, I am having trouble with part (b). I was thinking that you should use the equation:
F=k(q_1)(q_2)/r^2 , but I'm not really sure how to proceed. I would appreciate any help. Thanks so much!

2. Jan 21, 2005

### rbj

$$F = \frac{1}{4 \pi \epsilon_0} \times \frac{|q_1| |q_2|}{r^2}$$

if the amount of charge removed from one sphere is the same as what is added to the other, then $$|q_1|=|q_2|$$. you know what $$F$$ and $$r$$ is, so solve for $$|q|^2$$.

Last edited: Jan 21, 2005
3. Jan 21, 2005

### Staff: Mentor

You are on the right track. Realize that q_1 and q_2 have the same magnitude, so you can write F=kq^2/r^2 and solve for q. Then, knowing the charge per electron, you can figure the number of electrons that must have been moved.

4. Jan 21, 2005

### eil2001

Thanks, but why should q_1 and q_2 have the same magnitude? And then how do you go from "q" to the number of electrons?

5. Jan 22, 2005

### Nylex

They're both copper spheres and contain the same number of electrons..

6. Jan 22, 2005

### Gokul43201

Staff Emeritus
The copper sphere were originally neutral, because they had as many electrons as protons.

By removing some n electrons from sphere 1, you give it a net positive charge, Q1 = ne (where e = magnitude of charge on an electron/proton = 1.6 * 10^-19 C), due to the n excess protons it now has.

Sphere 2, having gained these n excess electrons will now have a net negative charge Q2 = -ne, due to n excess electrons.

Q1 = ne, Q2 = -ne, so |Q2| = ne.

7. Jan 22, 2005

### dextercioby

If u get the "q" in Coulombs,then u can use the fact that electrons have negative charge to write
$$q=-|q|$$

then
q C---------------------->"x" electrons
$$-1.6 \cdot 10^{-19}C$$ ------------------>1 electron.

Solve for "x".

Daniel.