Coulomb's Law of two copper spheres

[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!

 

[rbj]

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!

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

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 $$|q|^2$$.

 

[Doc Al]

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!

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.

 

[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?

 

[Nylex]

Thanks, but why should q_1 and q_2 have the same magnitude?

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

 

[Gokul43201]

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?

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.

Does that answer both your questions ?

 

[dextercioby]

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?

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.