Find electronic force, this one is driving me crazy,

[nutriculium]

this one comes out of my homework question. I am not asking you guys helping me doing my homework, i had a thought but didn't work at all and i hope someone can tell me what is going on.

question:
Suppose the magnitude of the proton charge differs from the magnitude of the electron charge by a mere 1 part in 10^9, i.e., qp = −qe (1 + 10^−9).
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(a) What would be the force between two 2.0-mm-diameter copper spheres 1.8 cm apart? Assume that each copper atom has an equal number of electrons and protons.

(b) Would this amount of force be detectable? What can you conclude from the fact that no such forces are observed?

my method:


1\get Volume of copper ball V = r^3*4(pi )/3
2\get Mass using m = V/density
3\convert Mass to number of mole using mole = m/atomic_mass_cu = m/63.5
4\29*mole*avogadro_constant=29*mole*6.02e23 = total_number_proton = total_number_eletron

since qp = -qe(1+10E-9), qp - qe = -qe(10E-9)
plug in e = 1.6E-19c
than F = Q1Q2/r^2 = (1+10E-9)(qe^2)/r^2=(1+10E-9)(total_number-eletron)(1.6E-19)/r^2

my answer was wrong.
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also i have no idea why the force is not detectable, someone give a hint please?

 

[nutriculium]

F shoud be = Q1Q2/r^2 = (1+10E-9)(qe^2)/r^2=(1+10E-9)[(total_number-eletron)(1.6E-19)]^2/r^2

i got F = 3.84N which is an impossibly big number

 

[K^2]

Sounds reasonable, actually. Why do you think that is wrong? I think the whole point of the exercise is to show that if the charges weren't quite the same, you'd really notice.

 

[nutriculium]

Sounds reasonable, actually. Why do you think that is wrong? I think the whole point of the exercise is to show that if the charges weren't quite the same, you'd really notice.

thank you for reply. I submitted my answer and the system says i was wrong.

also i don't get why this force can not be observed

 

[dipstik]

well, the wording seems a bit wanky, considering that a sphere is hollow (a ball is solid), making it difficult to determine the number of copper atoms. is the sphere an atomic thickness thick?
because the gap is much larger than the sphere/ball things, you prolly don't have to integrate, but i had to integrate for most of the sphere problems i had to do in electrodynamics/statics... taht could be it...

another ambiguity is if the distance is center to center or edge to edge.

assuming center to center point charges i got 8e-15 N, which would induce an acceleration around 2E-10 m/s^2 aka really really slow... and getting slower as r dominates.,, but still detectable using a decent interferometer.

i figured the number of atoms and an extra 29*1.6E-19 C charge per billion atoms (using mass, density and Avag.#).

but my answer is way off nutriclium's, so there is reason to doubt my calculations.

 

[nutriculium]

well, the wording seems a bit wanky, considering that a sphere is hollow (a ball is solid), making it difficult to determine the number of copper atoms. is the sphere an atomic thickness thick?
because the gap is much larger than the sphere/ball things, you prolly don't have to integrate, but i had to integrate for most of the sphere problems i had to do in electrodynamics/statics... taht could be it...

another ambiguity is if the distance is center to center or edge to edge.

assuming center to center point charges i got 8e-15 N, which would induce an acceleration around 2E-10 m/s^2 aka really really slow... and getting slower as r dominates.,, but still detectable using a decent interferometer.

i figured the number of atoms and an extra 29*1.6E-19 C charge per billion atoms (using mass, density and Avag.#).

but my answer is way off nutriclium's, so there is reason to doubt my calculations.

do you use the same method as i do? I will check my calculation again anyway
I took the this question as the objects are balls in stead of hollowed sphere. for every Cu atom there is one free electron, maybe this is the key to approach?

 

[nutriculium]

about distance, i think it is edge to edge given that diameter isprovided